Let s Practice Geometry

5/23/2018 Let s Practice Geometry

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Let's Practice...

A resource for Teachers, Students, and Parents.

By: Brent Tuller


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Ray AB, AB


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ABCABDCBD


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HMK or KMH


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AB CD


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RT=TS Bisect10=x

LP=PM Bisect5=PMso LM=10

SQ=QT Midpoint4=x

MO=ON Midpoint

9=ON9+9=18

GH=HI Midpoint x+4=2x-6-x -x 4=x-6 +6 +6 10=x

True XZ=ZY so Z is the midpoint


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AE=CE Bisect5=x


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Acute, Scalene


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a2+b2=c2

82+72=x264+49=x2

113=x2113=x2

10.6in=x

a2+b2=c2

x2+92=112x2+81=121

-81 -81 x2=40 x2=40 x=6.3in


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a2+b2=c2

82+112=142

64+121=196185=196

True 289=289

a2+b2=c2

82+152=17264+225=289289=289

False 185196


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a

2

+b

2

=c

2

a2+b2=c2 a2+b2=c2


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3-4-5

Scale factor=2

Scale Factor=2

x=2*5

x=10


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3-4-5

Scale factor=9

x=9*5x=45


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P=7+5+7+12P=31cm

P=8+6+2+18+6+24P=64cm

a2+b2=c222+42=c24+16=c2

20=c2 20=c2

4.47=c

P=4.47+5+8+9+2P=28.47cm


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heig

ht

A= bh 2

A=bh

A=bh

Area=(base)(height)

Area=(base)(height)

base

heigh

t

base

base

height


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(diagonal 1)(diagonal 2) 2

Area= (base+top)(height)

2A= (b+t)h

2

base

top

height

Area= (d1)(d2) 2A=

diagon

al1

diag

onal

2

ra

diu

s

A=r2 A=()(radius2)

A=s2 A=side2

side


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RectangleA=bhA=(15cm)(3cm)A=45cm2


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TriangleA=bh/2A=(10cm)(5.7cm)/2A=57cm2/2A=28.5cm2

a2+b2=c2

42+h2=72

16+h2=49-16 -16

h2

=33 h2=33 h=5.7

h=5.7


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A=bh 72=9h

9 9 8in=h

A= bh 2 8h 2

2*46= *2

92=8h

8 811.5=h


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B=bhB=6*5B=30

V=BhV=30*8V=240in3

V=r2h

V=(62)10V=36*10V=360V1130.97in3


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B=bhB=4*5B=20V=1/3(Bh)V=1/3(20*9)V=1/3(180)=60cm2

V=1/3r2hV=1/3(32)4V=1/39*4V=1/3(36)V=13V40.84in3

3-4-5 righttriangle scalefactor 1. 1*4=4

B=1/2bhB=1/2(3*4)B=1/2(12)B=6V=1/3(Bh)V=1/3(6*5)V=1/3(15)=5ft3

4ft


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a2+b2=c2

52+42=c2

25+16=c2

41=c2

6.4=c4.6m

5m

5m

5m 4m

4m3m

3m

4m

4.6m

3m

4cm

15cm10cm-6cm=4cm

10cm+5cm=15cm

4cm 4cm

4cm

15cm

6cm 6cm

15cm

4cm

4cm

15cm

8cm

8cm

8cm

8cm

8cm

8cm

5cm

10cm10cm

6cm

a2+b2=c2 h2+32=1002

h2+9=100 -9 -9 h2=91 h=9.54

3in

9.54in

6in 6in 6in 6in

9.54in 9.54in

6in

6in


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51+38=89m ABD=89


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x+33=90

.

x+33=90-33-33

x=57


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x+2x=180 3x=180 3 3 x=60


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x+43=180-43 -43

x=137m DEF=137

x

43


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x=138 Vertical Angle Theorem x=75 Vertical Angle Theorem


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x+45=2x+19 Vertical Angle Theorem-x -x 45=x+19 -19 -19 26=x


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m SOT=m NOEVertical Angle Theorem

138=m NOE


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m HAE=m DASVertical Angle Theorem

x+24=2x-8-x -x 24=x-8 +8 +8 32=xm DAS=2x-8m DAS=2(32)-8m DAS=64-8m DAS=56


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alternate exterior angles

vertical angles


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Alternate interior, m 1=m 2


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Alternate interior

46=x


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Alternate exterior

2x+19=x+23

-x -x x+19=23 -19-19 x=4


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x

68

Correspondingm ACB=m EFC 68=m EFC


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Linear Pairm ACH+m DCH=180(x+24)+(x-8)=180 x+24+x-8=180 2x+16=180 -16 -16

x+24x-8

2x=1642 2x=82

m ACH=x+24m ACH=82+24

m ACH=106


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x+x+x=180Triangle Sum Theorem 3x=180 3 3 x=60

2x-12=60equilateral triangle

2x-12=60 +12 +12 2x=72 2 2

x=36

x+x+30=180Triangle Sum Theorem 2x+30=180 -30 -30 2x=150 2 2 x=75

2x-27=x+53 iscosceles triangle 2x-27=x+53 -x -x x-27=53 +27+27 x=80


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Triangle Sum Theorem24+88+x=180

112+x=180-112 -112

x=68


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112+x=180-112 -112 x=68 m A=68

18

94

x


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Triangle Sum Theoremx+2x+(x-16)=180x+2x+x-16=180

4x-16=180+16 +16

4x=196

4 4 x=49


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41+87+y=180

y=_________

_______+x=180

x=128


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m 1+m 2=m 3

114+38=x

152=x


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m 1+m 2=m 3 29+x=87 -29 -29 x=______


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m 1+m 2=m 3(x+3)+(x+4)=125 x+3+x+4=125 2x+7=125 -7 -7 2x=118 2 2 x=59


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m 1+m 2=m 3 m Z=x+71 (x+71)+x=6x m Z=(_____)+71

m Z=______+71 m Z=______

6x

x

x+71

48

93

x


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What could I use to find x?

B1: 53+m 1+x=180 triangle sumtheorem


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What could I use to find x?B1: x=m 7 correspondingWhat could I use to find m 7?B2: m 5=m 7 corresponding


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What could I use to find x?B1: m 2+71+x=180 triangle sumtheoremWhat could I use to find m 2?B2: m 1=m 2 vertical anglesWhat could I use to find m 1?B3: m 1+48+53=180 triangle sumtheorem


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How can I find x?B1: m 3=x alternateinterior anglesHow can I find m 3?B2: m 3+36+58=180triangle sum therorem

B2: m 3+36+58=180m 3+94=180

-94 -94 m 3=86

B1: m 3=x=18086=x


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s1+s2=s318+15>27

33>27 True!So... yes they do!

s1+s2=s387+91>456178>456 False!No triangle here!


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s1+s2=s34+7>1111>11 false!

no triangle

s1+s2=s32+5>97>9 False!no triangle


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max.=7+12=19 and the min. is 12-7=5 so 5


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max.=4+3=7min.=4-3=1

1in


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ASS


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BC EF givenC F given

AC DF given

So ABC DEF by SAS.


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Vertical Angles

Shared Line

CA BD givenCAD ADB given

AD AD shared lineSo CAD BDAby SAS.

So PQR TSR

by ASA.P T given

PR RT given PRQ SRT vertical


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False.... the triangles may not

be congruent.

False.... the triangles arecongruent, but the parts don'tcorrespond. They aren't thesame part.

True the triangles arecongruent by SSS. So,

M P because CPCTC.

TV=WY CPCTC13=x

C=m F CPCTC x+5=2x-7-x -x 5=x-7 +7 +7 12=x


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25

6x

= =

2(x)=5(6) 2x=30 2 2 x=15

57

x15= =

7(x)=5(15) 7x=75 7 7 x=10.71


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MNO~MPQ by AAAor...MNO~MPQ by AA

M M same angle MON MQP corresponding MNO MPQ corresponding


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3

4=

32

42

9

16

2

=

4

5=

43

53

64

125

3

=

16

25=

16

25

4

5=

8

27

8

27

2

3= =

3 3

3


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Corresponding Angles

x=71

Corresponding Angles

x+35=2x-21 -x -x

35=x-21+21 +21

56=x

8=2x2 24=x

x+10=2(x-6) x+10=2x-12 -x -x

10=x-12+12 +12

22=x

10=x x+9=2x+4

-x -x9=x+4

-4 -4 5=x


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If Amy goes to the store then she buys milk.

If two angles add to 180 then they are supplementary.

If x=2 then 2x=4.

p hypothesis q conclusion




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You can drive it to the store.

He has a tail.

90


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She lost her patients.


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a 45 angle

A scalene triangle Anne Hathaway(or any bruenette or red-head)

A student 30 and 40


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If an animal has a beak then it is agoose. -False, a robin has a beak.

If an animal is not a goose then itdoes not have a beak. -False, again, arobin has a beak.

If an animal does not have a beak

then it is not a goose. -True!

If a triangle has 3 equal sidesthen it is equilateral. -true

If a triangle is not equilateralthen it does not have 3 equal sides.

-true.

If a triangle does not

have 3 equal sides then it is notequilateral -true


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If a figure is a rhombus then it isa square.

If a figure is not a square then it isnot a rhombus.

If a figure is not a rhombus then it isnot a square.


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If two angles add to 90then they arecomplementary. - True

If two angles aren't complementarythen they don't add to 90. - True

If two angles don't add to 90 thenthey aren't complementary. -true


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If two lines in a plane never intersect then they are parallel.-True, the statement is bi-conditional.

If an angle is acute then it measures 28.-False, 38 is acute the statement is not bi-conditional.

Iff two lines are parallel then they never intersect.


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If a triangle has twocongruent sides then it is isoceles.

Iff a triangle is Isoceles then it has twocongruent sides.


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Statements ReasonsF1: AB DE 1. GivenF2: AC DF 2. GivenF3. BC EF 3. GivenB1. ABC DEF 4. SSS


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HO

A

H

O

A cos 63= A

H

cos 63= 17x

cos 63= 17x *x

x(cos 63)=17 cos 63 cos 63

x= 17c0s 63

x= 170.4540x37.44

H

O

A

tan 56= OA

tan 56=9x

tan 56=9x *x

x*

x(tan 56)= 9 tan 56 tan 56

x= 9tan 56

x= 91.4826

x6.07

sin 39= OH

sin 39=x27

*2727* sin 39=x27

27(sin 39)=x27(0.6293)=x 16.99x

A

H

O


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tanx=OA

89

tanx=

tanx=0.8889

x=tan-10.8889

tan-1* *tan-1

23

x=6

23

x=632

32

x=9

tanx=0.8889

tan2nd = x41.63

sinx= OH

913

sinx=

sinx=0.6923sin-1* *sin-1

x=sin-10.6923

x43.81

* *


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Tanx= 8 6


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x=6y=62

a

b=a

c=a2

a

b=a

c=a2

a

b=a

c=a2

x=4y=4

x=32

y=322y=34y=3*2y=6


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c=2a

c=2ac=2*23c=43 so..y=43

b=a3 c=2ac=2a4=2a2 22=ay=2

b=a3

a a

c=2ab=a3

a

c=2ab=a3

ab=a3b=23*3b=29 so..b=2*3b=6 so...x=6

b=a35=a33 353

=a

5 *33 *3

539

533

y= 533

x=2a

x=2533

x=1033

=a


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Rectangle

A B

CDRhombus

True

False


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n=6 and (n-2)180 so (6-2)180=4*180=720

n=6 and (n-2)180 so (6-2)180=4*180=720=120n 6 6 6

(n-2)180=2,340(n-2)180=2,340 180 180 n-2=13 +2 +2 n=15 sides

n=5(n-2)180(5-2)1803*180540

94+78+156+91+x=540 419+x=540 -419 -419

x=121

n=6(n-2)180(6-2)1804*180720

x+7+2x-31+x+24+2x+x-13+2x+11=720 9x-2=720 +2 +2

9x=722

9 9 x=80.22

n=5 (n-2)180n

(5-2)1805

108

2x+8=108 -8 -8 2x=100 2 2 x=50


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n=6(n-2)180(6-2)1804*180720

x+81+4x-10+x+35+5x-60+3x+23+x+21=720

15x+90=720 -90 -90

15x=630

15 15 x=42


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21+27+58+42+53+34+45+x=360 280+x=360 -280 -280 x=80

n=8 360 360=45

n 8

n=8360 n360

845

360n

=18360

n=18*nn* 360=18n 360=18n

18 1820=n so...20 sides

2x-15

2x-15=45 +15 +15 2x=60 2 2 x=30


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x=2cm because all radii in acircle are equal.

GI=4JK=5


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C=DC=721.99

C=2rC=29C=1856.55

mDEF+mDE=360mDEF+127=360 -127-127mDEF= 233


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m B=mAC x=35

2(m B)=mAC 2x=44 2 2 x=22

2(m B)=mAC2(75)=mAC 150=mAC

m D=mAC x=150

m D=mAB 86=mAB

x=1/2mAB x=1/2(86) x=43


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mIJK+mKLI=360 190+mKLI=360-190 -190 mKLI=170

m J=1/2mKLI x=1/2(170) x=85


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m R=1/2mQSm R=1/2(48)m R=24

m Q+m R+m S=180 x+24+65=180 x+89=180 -89 -89 x=91


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3x=6*23x=123 3 x=4

2(x+4)=1(x+10) 2x+8=x+5 -x -x x+8=10 -8 -8 x=2

AB=AC 8=x

EF=EG x+3=2x-5 -x -x 3=x-5 +5 +5 8=x


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10=x

3-4-5 right triangle

x=10

17+x=90-17 -17 x=73

134/2=mFG 67=mFG


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3-4-5 righttriangle

scale factor =2

4*2=8

x=8

m DCE+m ACD=90 35+m ACD=90 -35 -35 m ACD=55

90+48+x=180 138+x=180 -138 -138 x=42


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A (5,-6) B(-3,6) x

1y

1 x

2 y

2

x1+x

2y

1+y

2 2 2 5+(-3) -6+6 2 2

2 12 2 2 (1,6)=MP

A (5,-6) B(x2,y

2) C(4,3)

x1

y1

xm

ym

x1+x

2 2

y1+y

2 2

5+x2

2-6+y

2 2

=xm

=ym

=4 =3

5+x2

2-6+y

2 2=4 =32* *2 *22*

5+x2=8

-5 -5x

2=3

-6+y2=6

+6 +6y

2=12

(3,12)=B

A (5,7) B(-6,-5) x

1y

1 x

2 y

2

D=(x2-x

1)2+(y

2-y

1)2

D=(-6-5)2+(7-(-5))2

D=(-11)2+(12)2

D=121+144D=265D16.78


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A'

B'

C'

F'

D'

E'

H'I'

G'


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J'

L'

K'

O'

N'

M'

Q'

P'

R' Q"

P"

R"


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Let's Practice...

Answers...


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Line CD, CD

Segment EF, EFPoint G, G

Plane HAT Ray NI, NI

Ray ON, ONPoint I, I

Line ME, ME

Line WE, WE

Line KJ, KJ

Plane COW

Segment HI, HI

Point U, U Ray BO, BO

Plane OLE

Segment LM, LM

Segment XY, XY

Ray AB, AB


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ABC or CBA EFG or GFE or F

JIK or KIJ PNO or ONP

TRQ or QRT XVW or WVX

ACB or BCA

IGH, HGI or G

LKJ or JKL QPR or RPQ

UYT or TYUBGC or CGB


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NPO or OPN

RTU or UTR

VZX or XZV

ABD or DBA

EHI or IHE

KOM or MOKVYX or XYV

DCB or BCD OPJ or JPO

TSU or UST VZY or YZV

HMK or KMH


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A

B

C

D

E

F

H

I

J

G

K

L


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EH FG

JK LMH T

NR OR PR QR

SW UW,VW TW

AC DB,

DE EB

GL FK,

GIH FJH

QN OP,NO PQ

RSE USL

RSU ESLRS SL

RT WURTS UWV TRS WUV

AC DBDE EBAE EC

AB CD


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FG HGLM JIFGL HGJ

GT ET AT RT

AG RE

ST TQOU NPNP SQ

WR OKWO ORWKO RKO

C OA BR N

AB BC CD DE EA

GO DL,GD OL

GM FHGM LKFH LK

NO QPQ O

RT VT ST UT VRU RUV UST RST


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IK=KL Bisect7=x

OS=SQ Bisect13=x

PQ=QS Bisectx=9

FG=GH Midpoint

12=x

ST=TU Midpoint19=TU19+19=38

VW=WX Midpoint11=WX11+11=22

XY=YZ Midpoint18=YZ18+18=36

AE=CE Bisect5=x


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AB=BC Midpoint x-5=2x-12

-x -x -4=x-12 +12 +12 8=x

DH=HF Bisect x+4=2x-8

-x -x 4=x-8 +8 +8 12=x

JM=ML Bisect 2x+15=3x+4-2x -2x 15=x+4 -4 -4 11=x

NO=OP Midpoint x+4=2x-6-x -x 4=x-6 +6 +6 10=x

QR=RS Midpoint x+7=2x-10-x -x 7=x-10 +10 +10 17=x

GH=HI Midpoint 4x+11=2x+19-2x -2x 2x+11=19 -11-11 2x=8 2 2 x=4

JM=ML Bisect x+5=2x-7

-x -x 5=x-7 +7 +7 12=x

GH=HI Midpoint 3x-2=x+8 -x -x 2x-2=8 +2+2 2x=10 2 2 x=5


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Obtuse, Scalene

Acute, Scalene Acute, Isosceles

Equilateral Right, Scalene

Right, Scalene

Acute, Scalene Obtuse, Scalene

Obtuse, Isosceles

Equilateral

Acute, Scalene

Right, Isosceles

Acute, Isosceles

Acute, Scalene


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a2+b2=c272+32=x2

49+9=x2

58=x2 58=x2

7.6ft=x

a2+b2=c2102+102=x2

100+100=x2 200=x2 200=x2

14.1cm=x

a2+b2=c2x2+62=152

x2

+36=225 -36 -36 x2=189 x2=189 x=13.7mm

a2+b2=c2x2+262=382

x2+676=1444 -676 -676 x2=768 x2=768 x=27.7in

a2+b2=c2x2+902=982

x2+8100=9604 -8100 -8100 x2=1504

x2

=1504 x=38.8yd

a2+b2=c2232+x2=452529+x2=2025

-529 -529 x2=1496 x2=1496

x=38.7m


315/553

a2+b2=c2192+442=x2

361+1936=x2 2297=x2 2297=x2

47.9m=x

a2+b2=c2542+1132=x2

2916+12769=x2 25583=x2 25685=x2

125.2in=x

a2+b2=c232+42=x29+16=x2

25=x2 25=x2

5ft=x

a2+b2=c2132+922=x2

169+8464=x2 8633=x2 8633=x2

92.9mi=x

a2+b2=c2x2+62=8.52x2+36=72.25

-36 -36 x2=36.25 x2=36.25 x=6in

a2+b2=c2x2+312=672x2+961=4489

-961 -961 x2=3528 x2=3528 x=59.4mm


316/553

x

12in

16in

x

17in

23in

x

15m

45m x

6ft

19ft

x

55cm x

37mm

21mm79cm

a2+b2=c2162+122=x2

256+144=x2

400=x2 400=x2

20in=x

a2+b2=c2232+172=x2

529+289=x2

818=x2

818=x2

28.6in=x

a2+b2=c2792+552=x2

6241+3025=x2 9266=x2

9266=x

2

96.3cm=x

a2+b2=c2x2+152=452

x2+225=2025 -225 -225 x2=1800 x2=1800 x=42.4mm

a2+b2=c2x2+62=192

x2+36=361 -36 -36 x2=325 x2=325 x=18ft

a2+b2=c2x2+212=372

x2+441=1369 -441 -441

x

2

=928 x2=928 x=30.5mm


317/553

False 4001225

202+212=292

400+441=841 841=841

a2+b2=c2

True 841=841

a2+b2=c2 122+162=352

144+256=1,225 400=1,225

False 145169

a2+b2=c2 82+92=132

64+81=169 145=169

152+342=482

225+1,156=2,304 1,381=2,304

a2+b2=c2

False 1,3812,304

282+452=532

784+2,025=2,809 2,809=2,809

a2+b2=c2

True 2,809=2,809

1192+1202=1692

14,161+14,400=28,561 28,561=28,561

a2+b2=c2

True 28,561=28,561

622+732=942

3,844+5,329=8,836 9,173=8,836

a2+b2=c2

False 9,1738,836

202+992=1012

400+9,801=1,0201 10,201=10,201

a2+b2=c2

True 10,201=10,201


318/553

112+632=882

121+3,969=7,744 4,090=7,744

a2+b2=c2

False 4,0907,744

122+302=432

144+900=1,849 1,044=1,849

a2+b2=c2

False 1,0441,849

312+452=862

961+2,025=7,396 2,986=7,396

a2+b2=c2

False 2,9867,396

842+1872=2052

7,056+34,969=42,025 42,025=42,025

a2+b2=c2

True 42,025=42,025

462+652=802

2,116+4,225=6,400 6,341=6,400

a2+b2=c2

False 6,3416,400

282+322=602

784+1,024=3,600 1,808=3,600

a2+b2=c2

False 1,808,3,600

92+402=412

81+1,600=1,681 1,681=1,681

a2+b2=c2

True 1,681,=1,681

162+522=822

256+2,704=6,724 2,960=6,724

a2+b2=c2

False 2,9606,724


319/553

3-4-5

Scale factor=4

3-4-5

Scale factor=9

5-12-13

Scale factor=2

7-24-25

Scale factor=2

8-15-17

Scale factor=3

Scale Factor=3

x=3*4x=12

3-4-5

Scale factor=2

Scale Factor=2

x=2*5

x=10


320/553

3-4-5

Scale factor=7

3-4-5

Scale factor=3

3-4-5

Scale factor=5

3-4-5

Scale factor=6

3-4-5

Scale factor=8

5-12-13

Scale factor=11

3-4-5

Scale factor=11

8-15-17

Scale factor=2

5-12-13

Scale factor=2

5-12-13

Scale factor=3


321/553

3-4-5

Scale factor=4x=4*4x=16

3-4-5


5-12-13


3-4-5


3-4-5


8-15-17

Scale factor=1x=1*8

x=8

5-12-13

Scale factor=2x=2*5

x=10

3-4-5

Scale factor=9

x=9*5x=45


322/553

8-15-17


3-4-5


3-4-5


7-24-25


3-4-5


3-4-5


3-4-5


7-24-25

Scale factor=3x=3*7

x=21


323/553

7-24-25


3-4-5


5-12-13


3-4-5


3-4-5

Scale factor=11

x=11*4x=44

3-4-5


8-15-17Scale factor=2x=2*17x=34

8-15-17



324/553

3-4-5Scale factor=2h=2*4h=8

a2+b2=c292+h2=102

81+h2=100-81 -81 h2=19 h2=19 h=4.4


a2+b2=c292+h2=142

81+h2=196-81 -81 h2=115 h2=115 h=10.7


a2+b2=c2

172+h2=272289+h2=729-289 -289 h2=440 h2=440 h=21


325/553

5-12-13Scale factor=2s=2*13s=26


3-4-5Scale factor=5h=5*4

h=20

7-24-25Scale factor=1s=1*25

s=25

3-4-5

Scale factor=7s=7*5s=35

a2+b2=c292+82=s2

81+64=s2 145=s2 145=s2

s=12.


326/553

11+21+11+21=64 13+19+13+19=64

38+17+39+52=14614+2+5+19+5+4+14+25=88

36+19+27=827+17+11+9=44

426+449+236=1108 7*10=70


327/553

3-4-5 scale factor=4

a2+b2=c242+52=x2

16+25=x2 41=x2 41=x2

6.4=x

2010

10

12

paralellogram


1937-18=19

38

(37-6)+7

6.4+9+7+13+4=39.4

6.4

19+37+7+18+12+19=112

16+20+12=4810+12+10+12=44

38+45+7+55+37+96+6+4=288

(96+4)-45

55


8

19+23+17+8+29=96

12

19-7


328/553


34

34+33.1+16+14=97.1

25


16

24-8

(12)

24/2

13


32

32

32

square

8

10-2

(parallelogram)

a2+b2=c2a2+72=92

a2+49=81 -49 -49 a2=32 a2=32 a=5.7

4

13-9

5.7

5.7+9+4+11+10=39.7

17


10+17+10+17=54

17

32*4=128

13

13+24+13=50

13+25+7+4+16+9+8=82


329/553

5


5+3+7+6+4=25

8-15-17scale factor=2

34


25

25+27+24+20=96

a2+b2=c2a2+302=412

a2+900=1681 -900 -900 a2=781 a2=781 a=27.9

27.9

27.9+41+34+16=118.9

a2+b2=c2132+122=c2

169+144=c2 313=c2 313=c2

17.7=c


15

16

15

15+28+15+28=86

13

17.717.7

17.7+17.7+26=61.4

a2+b2=c2

5

2

+6

2

=c

2

25+36=c2 61=c2 61=c2

7.8=c

7.8

12+25+7+19+7.8=70.8

7

5


330/553

12

12*4=48in

14

14

11 11

11+14+11+14=50ft

27

27*4=108mm

3240


24

32+40+24=96m

17

17

9 9

9+17+9+17=52ft

49

4+8.1+9=21.1in

a2+b2=c2a2+42=92

a2+16=81 -16 -16 a2=65 a2=65 a=8.1

8.1


331/553

24*4=96mm

24 11

11

8.5 8.5

11+8.5+11+8.5=39in

915


9+15+12=36ft

19

19

66

6+19+6+19=50in

10

10

8 8

8+10+8+10=36in

725


24

7+24+25=56ft


332/553

ParallelogramA=bhA=(5in)(4in)A=20in2

TriangleA=bh/2A=(9cm)(17cm)/2A=153cm2/2A=76.5cm2

TrapezoidA=(b+t)h/2A=(6cm+15cm)(13cm)/2A=(21cm)(13cm)/2A=273cm2/2

A=136.5cm2

ParallelogramA=bh

A=(11cm)(7cm)A=77cm2

Trapezoid

A=(b+t)h/2A=(16cm+10cm)(9cm)/2A=(26cm)(9cm)/2A=234cm2/2A=117cm2



333/553


Trapezoid

A=(b+t)h/2A=(11cm+7cm)(13cm)/2A=(18cm)(13cm)/2A=234cm2/2A=117cm2


TriangleA=bh/2A=(13m)(24m)/2A=312m2/2A=156m2

TrapezoidA=(b+t)h/2A=(23ft+16ft)(10ft)/2A=(39ft)(10ft)/2A=390ft2/2A=195ft2

CircleA=r2

A=(8cm)2

A=64

cm

2

A=201cm2


334/553

Circle

A=r2A=(14cm)2

A=196cm2

A=615.75cm2

Triangle

A=bh/2A=(12m)(7m)/2A=84m2/2A=42m2

SquareA=s2

A=(16ft)

2

A=256ft2

Trapezoid

A=(b+t)h/2A=(17mi+13mi)(6mi)/2A=(30mi)(6mi)/2A=180mi2/2A=90mi2

TrapezoidA=(b+t)h/2A=(31mm+27mm)(13mm)/2A=(58mm)(13mm)/2A=754mm2/2A=377mm2

RhombusA=(d

1)(d

2)/2

A=(10yd)(6yd)/2A=60yd2/2A=30yd2


335/553

TrapezoidA=(b+t)h/2A=(21cm+13cm)(4.5cm)/2A=(34cm)(4.5cm)/2A=153cm2/2A=76.5cm2

TrapezoidA=(b+t)h/2A=(23in+15in)(7.1in)/2A=(38in)(7.1in)/2

A=269.8in

2

/2A=134.9in2

TriangleA=bh/2A=(24m)(13.4m)/2A=321.6m2/2A=160.8m2


h=4 3-4-5 rt. triangle

h=4

a2+b2=c2

72+h2=102

49+h

2

=100-49 -49 h2=51 h2=51 h=7.1

h=7.1

a2+b2=c2

122+h2=182 144+h2=324-144 -144 h2=180 h2=180 h=13.4

a2+b2=c2

42+h2=62

16+h2=36-16 -16 h2=20

h2=20 h=4.5

h=4.5

h=13.4

TriangleA=bh/2A=(10cm)(5.7cm)/2A=57cm2/2A=28.5cm2

a2+b2=c2

42+h2=72

16+h2=49-16 -16

h2

=33 h2=33 h=5.7

h=5.7


336/553

TrapezoidA=(b+t)h/2A=(54mi+34mi)(24mi)/2A=(88mi)(24mi)/2

A=2112mi2

/2A=1056mi2

TrapezoidA=(b+t)h/2A=(8.9mm+4mm)(7mm)/2A=(12.9mm)(7mm)/2A=90.3mm2/2A=45.2mm2

Rhombus

A=(d1)(d2)/2A=(10cm)(6cm)/2A=60cm2/2A=30cm2

ParallelogramA=bhA=(18ft)(5.7ft)A=102.6ft2

CircleA=r2

A=(17cm)2

A=289cm2A=907.9cm2

a2+b2=c2

72+h2=92 49+h2=81-49 -49 h2=32 h2=32 h=5.7

Find theradius r.

34=2r2 217=r

3-4-5 rt

triangle

4*6=24h=24mi

3-4-5 rttriangle

h=4cm

a2+b2=c2

72+h2=82

49+h2=64-49 -49 h2=17 h2=15 h=3.9

3-4-5 rttriangle

4*2=8h=8yd

RhombusA=(d

1)(d

2)/2

A=(16yd)(12yd)/2A=192yd2/2A=96yd2

h=4

h=5.7

r=17h=24

3.9

h=8


337/553

188=(18)(d2)18 1810.4ft=d

2

(13+t)2 2

(11+12)h 2

A=bh 15=5h 5 5 3in=h

A= bh 2 6h 2

2*32= *2

64=6h 6 610.7=h

A= bh 2 2h 2

2*8= *2

16=2h 2 2 8in=h

A= (b+t)h 2

2*68= *2

136=23h23 23 5.9=h

(23)h 2

(13+t)4 2

A= (b+t)h 2

87= 2

43.5=13+t-13 -13 30.5m=t

68=

87=

A= (d1)(d2) 2 (18)(d

2)

22*94= *2

A=bh 72=9h

9 9 8in=h

A= bh 2 8h 2

2*46= *2

92=8h

8 811.5=h


338/553

A= bh 2 4h 2

2*12= *2

A= bh 2 26b 2

2*98= *2

196=26b26 26 7.5in=b

24=4h 4 4 6mi=h

(b+9)11 2

A= (b+t)h 2

2*65= *2

130=(b+9)11 11 11

11.8=b+9-9 -9 2.8mm=b

(3+7)h

2

A= (b+t)h 2

2*19= *2

38=10h10 10 3.8in=h

(10)h 2

19=

62=(14)(d2

)14 144.4ft=d

2

A= (d1)(d2) 2 (14)(d

2)

22*31= *2

A=r2

64=r2

20.4=r2

4.5ft=r

A=r2

121=r2

38.5=r2

6.2in=r

A=s2

169=s2

169=s2

13m=s


339/553

bh7*321cm2

A=bh2*816cm2

7

3 2

8cm

8A=

+

A=42+12=54ft2

+

7

6

4

3A= +

bh7*642ft2

A=bh3*412ft2

+

3ft

A= +

17

10

4

7

a2+b2=c2

42+b2=72

16+b2=49

-16 -16 b2=33 b=5.74

bh17*10

170cm2

A=

1/2bh1/2(4*5.74)1/2(22.96)11.48in2

+

5.7

4

4in

A=702-91=611m2

A=

39

18 14

13

14m

13m

bh

18*39702m2A= -

1/2bh

1/2(13*14)1/2(182)91m2

A=

12

10 3

4bh12*10120cm2

A= -1/2bh1/2(3*4)1/2(12)6cm2

A=120-6=114cm2

3cm

4cm

A=

10

10 6

4

+

bh10*10100in2

A=1/2bh1/2(6*4)1/2(24)12in2

A=100+12=112in2+

4in

6in

A=21+16=37cm2

A=170+11.48=181.48in2


340/553

A= +

13

13

7

8

bh13*13169in2

A=bh8*756in2

+ A=169+56=225in2

8

19

7

154

A=

bh19*7133in2

A=bh4*1560in2

- A=133-60=73in2

bh10*10100in2

A=r222

12.57in2-

A=100-(12.57*4)A=100-50.28A=59.72in2

*4

10

10A= - - --

bh18*8144in2

A=

1/2bh

1/2(4*4)1/2(16)8in2

-

A=144-(8*4)

A=144-32A=112in2

*4

A= -

18

8

A=

32

16-

A=

1/2bh1/2(4*6)1/2(24)12ft2

-A=512-(12*2)A=512-24A=488ft2

*2bh32*16512ft2

A=

13

8-

A=

1/2bh1/2(3*4)1/2(12)6cm2

-A=6-(6*4)A=104-24A=80cm2

*4bh13*8104cm2


341/553

A=

5

-5 14

bh5*525cm2

A=bh1*44cm2

- A=25-4=21cm2 bh

23*15345cm2

A=bh7*642cm2

- A=345-42-10A=293cm2

bh5*210cm2

-

A=

23

15

7

65

2- -

7cm

23cm

bh21*12252cm2

A=1/2bh1/2(5*4)10cm2

- A=252-10-18A=224cm2bh6*318cm2

-

A=

21

12

4

63- -5

5

4

bh21*16336in2

A= 1/2bh1/2(6*4)12in2

- bh8*1080in2

-

A=

2116

4 10

8- -6

A=336-12-80A=244in2

4in

6in

bh15*9135cm2

A=bh4*520cm2

- A=135-20-18A=97cm2

bh6*318cm2

-

A= 94

56

3- -

15

6cm

bh20*12240in2

A= 1/2bh

1/2(9*12)54in2

- A=240-54-16

A=170in2-

A=

20

12 12 8- -

9

1/2bh1/2(4*8)16in2

4

4in

8in

9in

3-4-5 rt triangle 9in


342/553

B=bhB=4*6B=24

V=BhV=24*7V=168in3

B=bhB=10*9B=90V=BhV=90*15

V=1,350ft3

B=1/2bhB=1/2(11*13)B=1/2(143)B=71.5

V=BhV=71.5*21V=1,501.5m3

B=1/2bhB=1/2(5*8)B=1/2(40)B=20V=BhV=20*6V=120yd3

B=1/2bhB=1/2(19*6)

B=1/2(114)B=57V=BhV=57*17V=969yd3

V=BhV=86*17V=1,462in3

V=r2h

V=(22)9V=4*9

V=36V113.10in3

V=r2h

V=(92)18

V=81*18V=1458V4580.44cm3


343/553

B=bhB=7*4B=28V=BhV=28*2V=56m3

4m

B=1/2bhB=1/2(7.14*7)B=1/2(49.98)B=24.99V=BhV=24.99*5V=124.95ft3

a2+b2=c2

72+b2=102

49+b2=100-49 -49 b2=51 b=7.14

B=1/2bhB=1/2(6*8)B=1/2(48)B=24V=BhV=24*7

V=168cm3

a2+b2=c2

72+b2=112

49+b2=121-49 -49 b2=72 b=8.49

V=r2h

V=(92)6V=81*6V=486V1,526.81yd3

D=2r18=2r2 2 9=r

B=S2

B=82

B=64V=BhV=64*23V=1,472mm3

B=1/2bh

B=1/2(7*8.49)B=1/2(59.43)B=29.72V=BhV=29.72*11V=326.92in3

7.14m

6cm

8cm

3-4-5 right

triangle scalefactor 2. 3*2=6

8.49cm


344/553

V=r2h

V=(112)20V=121*20V=2420V7,602.65in3

D=2r22=2r2 211=r

B=bhB=8*16B=128V=BhV=128*9V=1,152ft3

B=1/2bhB=1/2(9*12)B=1/2(108)B=54V=BhV=54*13V=702ft3

3-4-5 righttriangle scale

factor 3. 3*3=9

11cm

9cm

30-60-90 triangle. 4, 43

B=1/2bhB=1/2(4*43)B=1/2(27.71)B=13.86V=BhV=13.86*8V=110.88cm3

B=bhB=16*31B=496V=BhV=496*84

V=41,664in3

Oh

sinx=

sin38=O66*

*6

6(sin38)=O6(.6257)=O 3.69=O

a2+b2=c2

3.692+b2=62

13.62+b2=36-13.62 -13.62

b2=22.38 b=4.73

B=1/2bhB=1/2(4.73*3.69)B=1/2(17.45)B=8.73V=BhV=8.73*10V=87.3m3

3.69m4.73m


345/553

B=bhB=12*7B=84

V=BhV=84*11V=924m3

B=1/2bhB=1/2(8*6)B=1/2(48)

B=24V=BhV=24*9V=216ft3

V=r2h

V=(182)21V=324*21V=6804V21,375.4in3

B=bhB=23*28B=644V=BhV=644*11V=7,084cm3

B=S2

B=92B=81V=BhV=81*10V=810yd3

V=BhV=45*13

V=585mm3

B=S2

B=212B=441V=BhV=441*21V=9,261yd3

B=1/2bhB=1/2(6*8)B=1/2(48)B=24V=BhV=24*7V=168ft3



346/553

B=bhB=3*6B=18V=1/3(Bh)V=1/3(18*8)V=1/3(144)=48cm2

B=1/2bhB=1/2(7*9)B=1/2(63)B=31.5V=1/3(Bh)V=1/3(31.5*8)V=1/3(252)V=84ft3

V=1/3r2hV=1/3(52)11

V=1/325*11V=1/3(275)V=91.67V287.99in3

B=s2

B=62

B=36V=1/3(Bh)V=1/3(36*10)

V=1/3(360)V=120ft2

B=1/2bhB=1/2(13*18)B=1/2(234)B=117

V=1/3(Bh)V=1/3(117*15)V=1/3(1755)V=585mm3

V=1/3r2hV=1/3(122)24V=1/3144*24V=1/3(3456)

V=1152V3,619.11cm3

B=s2

B=32

B=9V=1/3(Bh)V=1/3(9*4)V=1/3(36)V=12ft2

V=1/3(Bh)

V=1/3(35*4)V=1/3(140)V=46.67ft2


347/553

B=1/2bhB=1/2(3*4)B=1/2(12)B=6V=1/3(Bh)

V=1/3(6*6)V=1/3(36)V=12ft3


3ft

5.6

7ft

a2+b2=c2

72+h2=92

49+h2=81-49 -49 h2=32 h=5.67

B=bhB=7*8B=56V=1/3(Bh)V=1/3(56*5.67)V=1/3(317.52)V=105.84ft3


B=1/2bhB=1/2(6*8)B=1/2(48)B=24V=1/3(Bh)V=1/3(24*8)V=1/3(192)V=64cm3

V=1/3r2hV=1/3(92)23V=1/381*23V=1/3(1,863)V=621V1,950.93in3

d=2r18=2r2 2

9=r

V=1/3r2h

V=1/3

(6

2

)12V=1/336*12V=1/3(432)V=144V452.39m3

d=2r12=2r2 2 6=r

B=s2

B=52

B=25V=1/3(Bh)V=1/3(25*4.9)V=1/3(122.5)V=40.83cm2

a2+b2=c2 52+h2=72

25+h2=49-25 -25 h2=24 h=4.9

6cm

6m

4.9cm


348/553

a2+b2=c2

42+h2=112

16+h2=121-16 -16 h2=105

h=10.25

B=bhB=8*9B=72V=1/3(Bh)V=1/3(72*10.25)V=1/3(738)V=246in3

B=1/2bhB=1/2(6*6)B=1/2(36)B=18V=1/3(Bh)V=1/3(18*7)V=1/3(126)V=42in3

45-45-90 righttriangle b=6

10.25in

6in

a2+b2=c2

62

+h2

=132

36+h2=169-36 -36 h2=133 h=11.53

11.53cm

B=bhB=7*10B=70V=1/3(Bh)V=1/3(70*11.53)V=1/3(807.1)

V=269.3cm3

V=1/3r2hV=1/3(82)14V=1/364*14V=1/3(896)V=144V2,814.87m3

d=2r16=2r2 2 8=r

8ft


B=1/2bhB=1/2(9*12)B=1/2(108)B=54V=1/3(Bh)V=1/3(54*11)V=1/3(594)V=198ft3

12ft

a2+b2=c2

92+h2=262

81+h2=676-81 -81 h2=595 h=24.39

24.39m

B=s2

B=172

B=289V=1/3(Bh)V=1/3(289*24.39)V=1/3(7048.71)V=2,349.57m3


349/553

V=1/3r2hV=1/3(42)14V=1/316*14V=1/3(224)V=74.67V234.58m3

10

.25cm

a2+b2=c2

82+h2=132

64+h2=169-64 -64 h2=105

h=10.25

d=2r8=2r2 2 4=r

4cm

16=8 bisect2

8cm

a2+b2=c2

82+h2=92

64+h2=81-64 -64 h2=17 h=4.12

B=bhB=12*11B=132V=1/3(Bh)V=1/3(132*4.12)V=1/3(543.84)V=181.28cm3

4.12cm

45-45-90 right

triangle

8in8in

B=1/2bhB=1/2(8*8)B=1/2(64)B=32V=1/3(Bh)V=1/3(32*8)V=1/3(256)V=85.33in3

82=42 bisect2

42ft

a2+b2=c2

(42)2

+h2

=112

(16*2)+h2=121 32+h2=121-32 -32 h2=89 h=9.43

9.43ft

B=s2

B=82

B=64V=1/3(Bh)V=1/3(64*9.43)

V=1/3(603.52)V=201.17ft3

45-45-90 righttriangle

3in

a2+b2=c2

32+h2=62

9+h2=36-9 -9 h2=27 h=5.2

5.2in

B=s2

B=(32)2

B=9*2B=18V=1/3(Bh)V=1/3(18*5.2)V=1/3(93.6)V=31.2in3

45-45-90 righttriangle

42in

42in

square

a2+b2=c2

42+h2=72

16+h2=49-16 -16 h2=33 h=5.74

B=s2

B=(42)2

B=16*2B=32V=1/3(Bh)V=1/3(32*5.74)V=1/3(183.68)V=61.23in3


350/553

45-45-90 righttriangle digonal=72

72=3.524.952

h=4.953h8.57

B=s2

B=(32)2

B=9*2B=18V=1/3(Bh)V=1/3(18*5.2)

V=1/3(93.6)V=31.2in3

45-45-90 righttriangle diagonal=9292=4.526.362

tan65=

4.95in

8.57in

h6.36

tan65= h6.36

*6.366.36*

6.36

6.36(tan65)=h6.36(2.1445)=h

13.64h

B=s2

B=92

B=81V=1/3(Bh)V=1/3(18*13.64)V=1/3(1104.84)V=368.28cm3

13.64cm

45-45-90 righttriangle diagonal=9282=425.662

5.66

tan42= h5.66

tan42= h6.36 *5.665.66*

5.66(tan42)=h5.66(.9004)=h 5.1h

5.1ft

B=s2

B=82B=64V=1/3(Bh)V=1/3(64*5.1)V=1/3(326.4)V=108.8ft3

a2+b2=c2

62+92=d2

36+81=d2

117=d2

10.82=d10.82=5.41 2

4.23m

5.41m

tan38= h5.41

tan38= h6.36

*5.45.41*

5.41(tan38)=h5.41(.7813)=h 4.23h

B=bhB=6*9B=56V=1/3(Bh)V=1/3(56*4.23)V=1/3(236.88)V=78.96m3


351/553

B=bhB=9*8B=72

V=1/3(Bh)V=1/3(72*11)V=1/3(792)V=264ft3

V=1/3r2hV=1/3(52)14V=1/325*13

V=1/3(325

)V=108.33V340.34ft3

V=1/3r2hV=1/3(62)14V=1/336*12V=1/3(432)V=144V1,021.02ft3

d=2r12=2r2 2 6=r

B=s2

B=72

B=49V=1/3(Bh)V=1/3(49*2)V=1/3(98)V=32.67in3

B=1/2bhB=1/2(5*14)B=1/2(70)B=35V=1/3(Bh)V=1/3(35*15)V=1/3(525)V=175cm3

B=1/2bhB=1/2(5*12)B=1/2(60)B=30V=1/3(Bh)V=1/3(30*11)V=1/3(330)V=110cm3

5-12-13 righttriangle scalefactor 1 12*1=12


352/553

d=2r8=2r2 24=r

4cm

3-4-5 righttriangle scalefactor=2

5*2=10

a2+b2=c2

a2+72=122

a2+49=144 -49 -49 a2=95 a=9.75

30-60-90right triangle

1053

11in

11in11in

11in

9in

9in

9in 9in

6in 6in

6in

6in

4cm

4cm

4cm

10m 10m

10m

10m

8m 6m

10m

10m 10m

9.75ft

6m 8m

8m6m

9.75ft

7ft

7ft

7ft

13ft 13ft

12ft

12ft

12ft13ft

9.75ft

10in10in

10in

10in

8in

8in8in

5in

5in

5in53in53in

53in


353/553

11-4=7

4+6=10

27-13=14

19-11=8

18-8=10

12-5=7

10cm

7cm 10cm 7cm6cm

6cm

6cm

8cm

8cm

8cm 8cm

8cm

8cm

4cm

4cm

4cm

4cm

4cm 4cm

11cm

11cm 11cm

11ft

11ft 11ft

13ft

13ft

13ft

19ft

19ft

19ft 27ft

27ft

27ft14ft

14ft

14ft

8ft

8ft 8ft8ft

8ft8ft

8ft

8ft

8ft

18cm

18cm12cm

8cm

10cm

8cm

10cm

7cm

7cm

5cm

5cm

18cm

10cm

8cm

7cm

5cm

6cm

6cm

6cm

6cm

6cm6cm

4/2=2

a2+b2=c2

a2+22=82

a2+4=64 -4 -4 a2=60 a=7.75

14ft

8ft

7.75in

2in

4in 4in 4in 4in

4in

4in

7.7

5in

7.7

5in

7.7

5in

7.7

5in

3-4-5 rt.triangle. scalefactor =1h=4

45-45-90 triangle62

62in

a2+b2=c2

a2+322=52

a2+18=25 -18 -18 a2=7 a=2.65

4in

6in

4in

6in 62in2.6

5in

6in

6in


354/553

6in

5in

6in

5in 5in

5in6in 6in

9in

9in 9in 9in

8ft

8ft

8ft

8ft

8ft 8ft 8ft

8ft

16ft

16ft 16ft 16ft

12cm 16cm 12cm 16cm

3-4-5 right

trianglescale factor=45*4=20

20cm 20cm

20cm

20cm

12cm16cm

24cm

24cm

2

4cm

5ft

5ft

5ft15ft

30in2 30in2 45in2

45in254in2 54in2

384cm

2

288cm

2

480cm

2

96cm2 96cm2

78.54ft2

52

78.54ft2

52 2(5)(15)

471.24ft2

64ft2 64ft2

128ft

2

128ft

2

128ft

2

128ft

2

30+30+45+45+54+54=258in2

96+96+384+288+480=1,344cm2

78.54+78.54+471.24=628.32ft2

64+64+128+128+128+128=640ft2


355/553

14-5=9

16-9=7

22-13=9

11-4=7

9in

5in

9in 9in

5in

16in

9in16in 5in

7in

7in

7in7in

7in

7in

7in

9in

9in

14in16in

7in

9in

7in

13in

13in

4in 4in22in

22in

7in

6in

6in

6in6in 6in 6in

11in

13in

22in4in 9in 7in

7in

9in

10/2=5

a2+b2=c2

a2+42=102

a2+16=100 -16 -16 a2=84 a=9.17

3-4-5 righttrianglescale factor=25*2=10

a2

+b2

=c2

a2+42=92

a2+16=81 -16-16 a2=65 a=8.06

8/2=410m

a2+b2=c2

a2+32=92

a2+9=81 -9 -9 a2=72 a=8.49

6/2=3

a2+b2=c2

a2+52=92

a2+25=81 -25 -25 a2=56 a=7.48

10/2=5

8cm9.1

7cm

8cm9.1

7cm

8cm9.1

7cm

8cm9.1

7cm

8cm

8cm

8m

10m6m

6m

8m

10m8.4

9m

7.48

m

8.0

6m

81in

2

81in

2

80in

235in

2

63in

2

49in

2

98in2112in2

63

in2

64cm2

24m2

25.47m2

32.24m2

37.4m2

24in

2

54in2 42in2

132in2

78in2154in2

154in2

52in2

52in2

66in2

81+80+81+80+35+63+49+98+112+63=742in2

36.68+36.68+36.68+36.68+64=210.72cm2

24+32.24+25.47+37.4=119.11m2

154+52+154+52+66+24+54+42+78+132=808in2

36.68cm2 36.68cm236.68cm236.68cm2

80in

2


356/553

10-2=8

7+1=8

8in 8in

7in7in

2in1in1in

8in

8in

6in

6in

6in

6in 6in6in

10in 8in2in7inin

8in

8in

4.5cm

4.5cm

4.5cm 11cm

9/2=4.5

a2+b2=c2

a2+22=92

a2+4=81 -4 -4 a2=77

a=8.77

4/2=2 a2+b2=c2

a2+2.52=92

a2+6.25=81 -6.25-6.25 a2=74.75 a=8.65

5/2=2.5

4.5cm

45-45-90triangle3

3ft3ft

3ft

3ft

3ft

3ft

3ft 3ft

6ft6ft

6ft

32ft

4ft 5ft

4ft

5ft

8.6

5ft

8.7

7ft

63.62cm2

4.52 2(4.5)(11)

311.02cm263.62cm2

4.52

17.54ft2 21.63ft2

4ft

5ft

8.6

5ft

8.7

7ft17.54ft

2

21.63ft2

20ft2

4.5ft2 4.5ft2

25.46ft2

18ft2 18ft2

42in2

48in260in2

64in2 64in2

12in2

2in

1in6in2

8in

48in2

63.62+63.62+311.02=438.26cm2

17.54+21.63+21.63+17.54+20=98.34cm2

4.5+4.5+18+18+25.46=70.46ft2

64+2+64+2+6+42+60+12+46+48=348in2

2in2 2in2


357/553


358/553


359/553

31+43=74m ABD=74

163-44=119m CBD=119

125-36=89

m CBD=89

78-21=57m CBD=57

112-29=83m ABD=83

97-48=49

m CBD=49

42+35=77m ABD=77

51+38=89m ABD=89


360/553

45+49=96

m ABD=94

119-67=52m CBD=52

115+65=180m ABC=180

123-67=56m CBD=56

58+37+59=154

m ABE=154

22+28+78=128m ABE=128

61+25+15=101

m ABE=101

25+41+36=102m ABE=102


361/553

111-31-52=28m CBD=28

136-35-42=59m ABC=59

170-21-19-23=107m CBD=107

58+48+31+43=180m ABF=180

136-67=69

m DBE=69

(77+89)-136=30

m CBD=30

169-39-26-23=107

m DBE=81 165-36-21-57=51m CBD=51


362/553

Two angles whose measures

add to 90.

Two angles who are supplementary

and adjacent.

Two angles whose measures

add to 180.


363/553

y+134=180

-134-134

y=46

z+67=180-67 -67 z=113

z+67=180-67 -67 z=113 x+64=90

-64-64

x=26

y+44=180-44 -44 y=136

z+90=180-90 -90 z=90

x+12=90-12 -12 x=78

x+64=180-64 -64 x=116

x+33=90

.

x+33=90-33-33

x=57


364/553

x+(3x+18)=90 x+3x+18=90 4x+18=90 -18-18 4x=72

4 4 x=18

(x+21)+(x+58)=180 x+21+x+58=180 2x+79=180 -79 -79 2x=101 2 2 x=50.5

(2x+8)+(x-24)=180 2x+8+x-24=180 3x-16=180 +16 +16 3x=196 3 3 x=65.3

(x+15)+(x-12)=180 x+15+x-12=180

2x+3=180 -3 -3 2x=177 2 2 x=88.5

131+y=180-131 -131 y=49

49+x=180 -49 -49

x=131

The value of x is the same asthe measure of the angle onthe other side of theintersecting lines, 131.

x+2x=180 3x=180 3 3 x=60


365/553

143+x=180 linear pair

-143 -143x=37

m TRS=37

x143

59+x=90-59 -59

x=31

m H=31x

59

x

78 78+x=180-78 -78

x=102

m O=102

x+27

x (x+27)+x=180 linear pair x+27+x=180 2x+27=180

-27 -272x=153 2 2 x=76.5

m ROK=76.5

2x+11

(2x+11)+x=180 linear pair 2x+11+x=180

3x+11=180 -11 -113x=169

3 3 x=56.3

check your work

x

x+43=180-43 -43

x=137m DEF=137

x

43


366/553



x=48 Vertical Angle Theorem

x=90 Vertical Angle Theorem


367/553

x+13=2x-23 Vertical Angle Theorem-x -x 13=x-23 +23 +23 36=x

x+117=3x+9 Vertical Angle Theorem-x -x 117=2x-9 +9 +9 126=2x 2 2

63=x

2x-17=x+12 Vertical Angle Theorem-x -x x-17=12 +17 +17 x=29

x+91=3x-37 Vertical Angle Theorem-x -x 91=2x-37

+37 +37 128=2x 2 2 64=x

x+33=2x-23 Vertical Angle Theorem-x -x 33=x-23 +23 +23 56=x

x+45=2x+19 Vertical Angle Theorem-x -x 45=x+19 -19 -19 26=x


368/553

m EAM=m IALVertical Angle Theorem

63=m IAL

m TKE=m AKSVertical Angle Theorem

87=m AKS

m GER=m AETVertical Angle Theorem147=m AET

m IKS=m HKEVertical Angle Theorem

51=m HKE

m DCE=m ACBVertical Angle Theorem

153=m ACB

87

138

63

147

51 153

m SOT=m NOEVertical Angle Theorem

138=m NOE


369/553

m ABD=m CBEVertical Angle Theorem

2x-37=x+65-x -x x-37=+65 +37 +37 x=102

m CBE=x+65m CBE=102+65m CBE=102+65m CBE=167

m GET=m AENVertical Angle Theorem 3x-51=2x-17-2x -2x x-51=-17 +51 +51 x=34m GET=3x-51m GET=3(34)-51m GET=102-51

m GET=51

m BOE=m NOLVertical Angle Theorem

5x+36=3x+42-3x -3x 2x+36=42 -36-36 2x=6

2 2 x=3m NOL=3x+42m NOL=3(3)+42m NOL=9+42m NOL=51

m LEN=m BEDVertical Angle Theorem

X+89=2x+89-x -x 89=x+89 -89 -89

0 =x

m BED=2X+89m BED=2(0)+89m BED=0+89m BED=89

m LIO=3xm LIO=3(51)m LIO=153

m PIT=m LIOVertical Angle Theorem

4X-51=3X-3x -3x x-51=0 +51 +51 x=51

x+24

2x-8

2x-37 x+65

3x-512

x-17 x+89

2x+89

5x+363x+42

4x-51

3x

m HAE=m DASVertical Angle Theorem

x+24=2x-8

-x -x 24=x-8 +8 +8 32=xm DAS=2x-8m DAS=2(32)-8m DAS=64-8m DAS=56


370/553

1,2; 2,3; 3,4; 4,5; 5,1

1,3;

1,2; 2,3

1,2; 2,3; 3,4; 4,5; 5,6; 6,1

1,4; 2,5; 3,6

1,2;2,3;3,4;4,5;5,6;6,7;7,8;8,1

1,5; 2,6; 3,7; 4,8

1,2; 2,3; 3,4; 4,5; 5,6; 6,7; 7,8 8,1

1,2; 3,4; 5,6; 7,8


371/553

linear pair

vertical angles

adjacent angles

supplementary

complementary

linear pair

vertical angles

complementary

linear pair

supplementary

vertical angles

vertical angles

complementary

vertical angles

supplementary

two angles that are supplementary and adjacent

two angles that share a common ray and vertex

two angles that are on opposite sides of two intersecting lines

complementary


372/553

1, 5; 3, 7; 2, 6; 4, 8

3, 6; 4, 5;

1, 8; 2, 7;

3, 5; 4, 6;


373/553


374/553

consecutive angles

corresponding angles corresponding angles

corresponding angles alternate interior angles

alternate exterior angles alternate interior angles

consecutive angles corresponding angles

a linear pair, or supplementary

vertical angles

corresponding angles vertical angles

alternate interior angles

a linear pair, or supplementary a linear pair, or supplementary

alternate exterior angles

vertical angles


375/553

G

D

I

E

C

B

F

A

H


376/553

Corresponding, m 1=m 2



Alternate exterior, m 1=m 2

Alternate exterior, m 1=m 2

Consecutive, m 1+m 2=180


Consecutive, m 1+m 2=180



377/553

Corresponding

111=x

Alternate exterior

x=37

Corresponding

175=x

Alternate interior

x=58

Corresponding

x=26

Consecutive

x+68=180-68 -68 x=112

Alternate interior

46=x


378/553

Corresponding

x=31

Alternate interior

x=83

Vertical

x=126

Alternate interior

x=132

Corresponding

x=119

Alternate exterior

x=96

Linear Pair

x+113=180-113 -113 x=67

Consecutive

x+21=180-21 -21 x=159


379/553

Corresponding

2x-61=x+3 -x -x x-61=3 +61+61 x=64

Alternate interior

2x-12=x+34 -x -x x-12=34 +12+12 x=46

Vertical

3x+21=x+57 -x -x 2x+21=57 -21-21 2x=36 2 2

x=18

Corresponding

3x-35=2x+52-2x -2x x-35=52 +35 +35 x=87

Consecutive

(2x+42)+(x-23)=180 2x+42+x-24=180 3x+18=180 -18 -18 3x=162 3 3 x= 54

Linear pair

(x+23)+(x+61)=180 x+23+x+61=180

2x+84=180 -84 -84 2x=96 2 2 x= 48

Alternate exterior

2x+19=x+23

-x -x x+19=23 -19-19 x=4


380/553

Vertical

2x-17=x+27 -x -x x-17=27 +17+17

x=44

Corresponding

2x-37=x+79 -x -x x-37=79 +37+37 x=116

Alternate interior

2x+5=x+59 -x -x x+5=59 -5 -5 x=54

Corresponding

2x+17=x+77 -x -x x+17=77 -17-17 x=60

Alternate exterior

3x-26=x+64 -x -x 2x-26=64 +26+26 2x=90

2 2 x=45

Vertical

2x+32=x+97 -x -x x+32=97 -32-32 x=65

Corresponding

3x+71=5x+37-3x -3x 71=2x+37 -37 -37 34=2x

2 217=x

Consecutive

(x+23)+(x+54)=180 x+23+x+54=180 2x+77=180 -77 -77 2x=10 3 2 2 x=5 1.5


381/553

x

x

x

x

x

x

85

91103

47

63

Alternate exterior

m HFG=m BCD 103=m BCD

Vertical

m GEH=m BEF 47=m BCD Linear Pair

m DCH+m ACH=180 103+x=180-103 -103 x=77 m ACH=77

Alternate interior

m DCH=m BFE 85=m BFE

Consecutivem EFB+m DCH=180

91+x=180-91 -91 x=89 m ACH=89

x

68

Correspondingm ACB=m EFC 68=m EFC


382/553

Alternate Exterior

m ACB=m HFG2x-45=x+23-x -x

x-45=23 +45+45 x=68m HFG=x+23m HFG=68+23m HFG=91

2x-45

x+23

Corresponding

m EFH=m ACH2x-142=x+16-x -x x-142=x-16 +142 +142 x=126m ACH=x-16m ACH=126-16

m ACH=110

Corresponding

m BCD=m BFG x+26=2x-24-x -x 26=x-24 +24 +24

50=xm BFG=2x-24m BFG=2(50)-24m BFG=100-24m BFG=76

Alternate Interior

m ADF=m HEC2x+4=4x-14-2x -2x 4=2x-14 +14 +14 18=2x

2 2 9=xm HEC=4x-14m HEC=4(9)-14m HEC=36-14m HEC=22

Consecutive

m GF+m DCH=180(x+32)+(x+24)=180 x+32+x+24=180

2x=164

2x+56=180 -56 -56 2x=124 2 2 x=62

m DCH=x+24m DCH=62+24

m DCH=86

2x-124x+16

x+32

x+24

x+26

2x-242x+4

4

x-14

Linear Pairm ACH+m DCH=180(x+24)+(x-8)=180 x+24+x-8=180 2x+16=180 -16 -16

x+24x-8

2x=1642 2x=82

m ACH=x+24m ACH=82+24

m ACH=106


383/553

AB CD 1 and 2 arecorresponding so m 1=m 2

AB CD 1 and 2 are Alternateexterior so m 1=m 2

AB CD 1 and 2 arecorresponding so m 1=m 2

AB CD 1 and 2 are Alternateinterior so m 1=m 2

AB is not to CD 1 m 1=m 2 isfalse.

AB is not to CD 1 som 1=m 2 is false.


384/553

AB is not to CD 1 and 2 are

m 1=m 2 is false.

AB is not to CD som 1+m 2=180 is false.

This is true because vertical

angles are always equal.

AB CD, 1 and 2 areconsecutive so m 1+m 2=180 istrue.

1 and 2 are Corresponding ifcorresponding angles are equal

then AB CD.

1 and 2 are Alternateexterior if Alternate exterior

angles are equal then AB CD.

1 and 2 are Alternate interior

if Alternate interior angles areequal then AB CD

1 and 2 are Vertical angles.Vertical angles don't requireparallel lines so we don't know ifAB CD so probably false.


385/553


386/553


91+x=180-91 -91

x=89


129+x=180-129 -129

x=51

Triangle Sum Theorem

31+53+x=18084+x=180-84 -84

x=96


150+x=180-150 -150

x=30


51+x=180-51 -51

x=129


72+x=180-72 -72

x=108


165+x=180-165 -165

x=15


112+x=180-112 -112

x=68


387/553


121+x=180-121 -121

x=59

Triangle SumTheorem24+x+x=18024+2x=180-24 -24 2x=156

2 2 x=78

Equilateral Triangle

x=60

Triangle Sum Theorem46+71+x=180117+x=180

-117 -117 x=63


62+x=180-62 -62

x=118


160+x=180-160 -160

x=20

Triangle Sum Theorem32+x+x=180

32+2x=180-32 -32 2x=148 2 2 x=74

Triangle Sum Theorem30+x+x=180

30+2x=180-30 -30 2x=150 2 2 x=75


388/553


120+x=180-120 -120

x=60

m G=60


155+x=180-155 -155

x=25 m M=25


90+x=180-90 -90 x=90 m H=90

Equilateral Trianglex=60m O=60m T=60m P=60


37+x=180-37 -37

x=143 m M=143


144+x=180-144 -144

x=36 m H=36

Triangle Sum Theorem 48+x+x=180

48+2x=180-48 -48

2x=132 2 2 x=66

m T=66

30

x

17

138x

43

47

x

48x x

x

24

13

x

26118

x

x

x


112+x=180-112 -112 x=68 m A=68

18

94

x


389/553

Triangle Sum Theoremx+3x+(x+15)=180x+3x+x+15=180

5x+15=180-15 -15

5x=165 5 5 x=33

Triangle Sum Theoremx+(x+43)+(x-31)=180x+x+43+x-31=180

3x+12=180-12 -12

3x=168 3 3 x=56

Triangle Sum Theoremx+x+(x-27)=180x+x+x-27=180

3x-27=180+27 +27 3x=207 3 3 x=69

Triangle Sum Theoremx+(x+55)+(x+38)=180x+x+55+x+38=180

3x+93=180-93 -93

3x=87 3 3 x=29

Triangle Sum Theorem(x+21)+(x+23)+(x+61)=180x+21+x+23+x+61=180

3x+105=180-105-105

3x=75 3 3 x=25

Triangle Sum Theoremx+2x+(x-16)=180x+2x+x-16=180

4x-16=180+16 +16

4x=196

4 4 x=49


390/553

Triangle Sum Theorem2x+(x-23)+(x-17)=1802x+x-23+x-17=180

4x-40=180+40 +40

4x=220 4 4 x=55 m S=2x m S=2(55)

m S=110

Triangle Sum Theorem2x+x+(2x+30)=1802x+x+2x+30=180

5x+30=180-30 -30

5x=150 5 5 x=30 m B=2x m B=2(30) m B=60

2x+30

2x

x

2x

x-23

x-17

x+5

x-7

x

x

x

3x+19

x-22

x-17

Triangle Sum Theorem90+(x-7)+(x+5)=18090+x-7+x+5=1802x+88=180

-88 -88 2x=92m Z=46-7 2 2 m Z=39 x=46 m Z=x-7

Equilateral Trianglex=60m R=60m Q=60m S=60

Triangle Sum Theorem(x-22)+(3x+19)+(x-17)=180

x-22+3x+19+x-17=1805x-20=180+20 +20

5x=200 5 5 x=40

m X=3x+19m X=3(40)+19m X=120+19m X=139


391/553

m 1+m 2=m 3

54+63=x

117=x

m 1+m 2=m 3

114+38=x

152=x


392/553

m 1+m 2=m 3

18+42=x

60=x

m 1+m 2=m 3

48+68=x

116=x

m 1+m 2=m 343+106=x 149=x

m 1+m 2=m 3

21+138=x 159=x

m 1+m 2=m 3 60+90=x 150=x

m 1+m 2=m 3 35+90=x 125=x


393/553

m 1+m 2=m 3 78+x=131 -78 -78

x=53

m 1+m 2=m 3 142+x=167 -142 -142

x=25

m 1+m 2=m 3 39+x=106 -39 -39

x=67

m 1+m 2=m 3 42+x=77 -42 -42

x=35

m 1+m 2=m 3 x+x=148 2x=148

2 2 x=74

58

m 1+m 2=m 3 29+x=87 -29 -29 x=______


394/553

m 1+m 2=m 3 (x-6)+x=148 x-6+x=148

2x-6=148 +6 +6 2x=154 2 2 x=77

m 1+m 2=m 3(2x-37)+90=3x 2x-37+90=3x 2x+53=3x -2x -2x

53=x

m 1+m 2=m 3(x+1)+(2x-17)=x+89 x+1+2x-17=x+89 3x-16=x+89 -x -x 2x-16=89 +16+16 2x=105 2 2 x=52.5

m 1+m 2=m 3(x+13)+(x+13)=135

2(x+13)=135 2x+26=135 -26 -26 2x=109 2 2 x=54.5

m 1+m 2=m 3(x+34)+(x+34)=3x 2(x+34)=3x 2x+68=3x -2x -2x 68=x

m 1+m 2=m 3(x+3)+(x+4)=125 x+3+x+4=125 2x+7=125 -7 -7 2x=118 2 2 x=59


395/553

m 1+m 2=m 3(x-16)+(x+3)=x+42 x-16+x+3=x+42 2x-13=x+42 -x -x x-13=42 +13+13 x=55

m 1+m 2=m 3(x-19)+(x-26)=x

x-19+x-26=x 2x-45=x -2x -2x -45=-x -1 -1 45=x

35

61

x

m 1+m 2=m 3 93+48=x

141=x

m 1+m 2=m 3 35+61=x 96=x

x+71+x=6x 2x+71=6x -2x -2x 71=4x 4 4 17.75=x

17.75

17.7578.75

m 1+m 2=m 3 m Z=x+71 (x+71)+x=6x m Z=(_____)+71

m Z=______+71 m Z=______

6x

x

x+71

48

93

x


396/553

x

422x+19

m 1+m 2=m 3 x+42=2x+19 -x -x 42=x+19 -19 -19 23=x

m 1+m 2=m 3 60+60=x 120=x

m ATS=x m ATS=120

m CAS=2x+19m CAS=2(23)+19m CAS=46+19m CAS=65

m 1+m 2=m 3 x+x=148 2x=148 2 2 x=74

m D=x

m D=74

x x

x60

60

60

1482x+51

4x+9

x

m 1+m 2=m 3(2x+51)+x=4x+9 2x+51+x=4x+9 3x+51=4x+9

-3x -3x 51=x+9 -9 -9 42=x

m HEP=4x+9m HEP=4(42)+9m HEP=168+9m HEP=177

75 3x+9

x

m GRE+m ERA=180 75+m ERA=180-75 -75 m ERA=105

105

m 1+m 2=m 3105+x=3x+9 -x -x 105=2x+9 -9 -9 96=2x 2 2 48=x

m HEP=3x+9m HEP=3(48)+m HEP=144+9m HEP=153


397/553


B1: m 7=x corresponding angles


B1: m 1=x corresponding angles What could I use to find x?

B1: m 2+m 3+x=180 triangle sumtheorem


B1: m 2+m 1+x=180 triangle sumtheorem


B1: m 9=x corresponding angles


B1: m 1+x=180 linear pair



*Note: Thereare manypossible waysto solve someof theseproblems.




398/553

What could I use to find x?B1: m 1+m 3=x remote exterior

angle theoremWhat could I use to find m 3?B2: m 3+132=180 linear pair

What could I use to find x?B1: m 2+61+x=180 triangle sumtheoremWhat could I use to find m 2?B2: m 1=m 2 vertical angles

*Note: There are many possibleways to solve some of theseproblems.


B1: m 7+68=x remote exteriorangle theoremWhat could I use to find m 7?B2: m 7+35=90 complementary

What could I use to find x?B1: m 2+m 3+x=180 triangle sumtheoremWhat could I use to find m 3?B2: m 3=53 corresponding angles

What could I use to find x?B1: m 2+m 5+x=180 angle additionpostulate, straight angleWhat could I use to find m 5?B2: m 5+76+18=180 triangle sumtheorem.

What could I use to find x?B1: x=m 7 correspondingWhat could I use to find m 7?B2: m 5=m 7 corresponding


399/553

What could I use to find x?B1: m 1+93+x=180 triangle sumtheoremWhat could I use to find m 1?B2: m 1+m 4+83=180 angleaddition postulateWhat could I use to find m 4?B3: m 4+132+24=180 trianglesum theorem


B1: m 9=x corresponding anglesWhat could I use to find m 9?B2: m 9=68 alternate interior angles

What could I use to find x?B1: m 10+m 13+x=180 trianglesum theoremWhat could I use to find m 10?B2: m 10+=42 vertical anglesWhat could I use to find m 13?B3: m 13=78 corresponding angles

What could I use to find x?B1: m 1+31=x=180 remote exteriorangle theoremWhat could I use to find m 1?B2: m 1+142=180 vertical angles

What could I use to find x?B1: m 1+82=x remote exterior angletheorem

What could I use to find m 1?B2: m 1+m 2+82=180 trianglesum theoremWhat could I use to find m 2?B3: m 2=32 alternate interior angles

What could I use to find x?B1: m 2+71+x=180 triangle sumtheoremWhat could I use to find m 2?B2: m 1=m 2 vertical anglesWhat could I use to find m 1?B3: m 1+48+53=180 triangle sumtheorem


400/553

How can I find x?B1: m 7+43=x remoteexterior angle theoremHow can I find m 7?B2: m 7+68=90complementary anglestriangle sum therorem

B2: m 7+68=90-68-68

m 7=22

B1: m 7+43=x22+43=x

65=x

How can I find x?B1: m 3=x vertical anglesHow can I find m 8?B2: m 3+39=180 linear

pair

B2: m 3+39=180 -39 -39 m 3=141

B1: m 3=x141=x

How can I find x?B1: m 1+m 2=x remoteexterior angle theoremHow can I find m 2?B2: m 2+142=180linear pairHow can I find m 1?B3: m 1+31+87=180angle addition postulate,straight angle

B3: m 1+31+87=180m 1+118=180

-118-118 m 1=62

B2: m 2+142=180-142 -142

m 2=38B1: m 1+m 2=x

38+62=x 100=x

How can I find x?B1: m 3=x alternateinterior anglesHow can I find m 3?B2: m 3+36+58=180triangle sum therorem

B2: m 3+36+58=180m 3+94=180

-94 -94 m 3=86

B1: m 3=x=18086=x


401/553

How can I find x?B1: m 13=x alternateexterior anglesHow can I find m 13?B2: m 13=163corresponding angles

B2: m 13=163

B1: m 13=x163=x

How can I find x?B1: m 1=x vertical anglesHow can I find m 1?B2: m 1+41+72=180

triangle sum theorem

B2: m 1+41+72=180m 1+113=180

-113-113 m 1=67

B1: m 1=x67=x

How can I find x?B1: m 1+m 4=x remoteexterior angle theoremHow can I find m 1?B2: m 1+72+68=180angle addition postulate,straight angleHow can I find m 4?B3: m 4=52 verticalangles

B3: m 4=52B2: m 1+72+68=180

m 1+140=180 -140-140 m 1=40B1: m 1+m 2=x

52+40=x 92=x

How can I find x?B1: (m 1+31)+(52+24)+x=180 triangle sumtheoremHow can I find m 1?B2: m 1+63+89=180triangle sum theorem

B2: m 1+63+89=180m 1+152=180

-152-152 m 1=28

B1:(m 1+31)+(52+24)=18028+31+52+24+x=180

135+x=180 -135 -135 x=45


402/553

How can I find x?B1: m 6+m 7=x remoteexterior angle theoremHow can I find m 6?B2: m 6+48=90complementary anglesHow can I find m 7?B3: m 7=53corresponding angles.

B3: m 7=53B2: m 6+48=90

-48-48 m 6=42B1: m 6+m 7=x

42+53=x 95=x

How can I find x?B1: m 1+55=x remoteexterior angle theoremHow can I find m 1?B2: m 1+46=90complementary angles

B2: m 1+46=90-46-46

m 6=44B1: m 1+55=x

44+55=x 99=x

How can I find x?B1: m 11+x=180 linearpairHow can I find m 11?B2: m 11+m10+20=180

triangle sum theoremHow can I find m 10?B3: m 10=78corresponding angles.

B3: m 10=78B2: m 11+m 10+20=180 m 11+78+20=180

m 11+98=180 -98-98

m 11=82B1: m 11+x=18082+x=180

-82 -82 98=x

How can I find x?B1: m 1+(38+26)+x=180triangle sum theorem

How can I find m 1?B2: m 1+139=180 linearpair

B2: m 1+139=180-139 -139

m 1=41B1: m 1+(38+26)+x=180 41+64+x=180

105+x=180 -105 -105 x=75


403/553

How can I find x?B1: m 5+41+x=180triangle sum theoremHow can I find m 5?B2: m 5=m 3How can I find the m 3?B3: 47+21+m 3=180

B2: m 3=m 5 112=m 5B1: m 5+38+x=180

112+38+x=180 150+x=180 -150 -150 x=30

How can I find x?B1: m 1+m 2+x=180triangle sum theoremHow can I find m 1?B2: m 1=72corresponding anglesHow can I find the m 2?B3: m 2=91 vertical

angles

B3: m 2=91

B2: m 1=72

B1: m 1+m 2+x=18091+72+x=180

163+x=180 -163 -163 x=17

How can I find x?B1: m 2+m3+x=180triangle sum theorem

How can I find m 2?B2: m 2=126corresponding anglesHow can I find the m 3?B3: m 3=44 alternateexterior angles

B3: m 3=44

B2: m 2=126

B1: m 2+m 3+x=180126+44+x=180

170+x=180 -170 -170 x=10

How can I find x?B1: m 2+96+x=180triangle sum theoremHow can I find m 2?B2:(m1+m 2)+69+72=180triangle sum theoremHow can I find the m 1?B3:69+90+m 1=180triangle sum theorem

B3: 69+90+m 1=180159+m 1=180

-159 -159 m 1=21

B2:(m1+m 2)+69+72=180

21+m 2+69+72=180 162+m 2=180 -162 -162 m 2=18

B1: m 2+96+x=18018+96+x=180

114+x=180 -114 -114 x=66

B1: 47+21+m 3=18047+21+m 3=180

68+m 3=180 -68 -68 m 3=112


404/553

How can I find x?B1: m 8=xcorresponding anglesHow can I find the m 8?B2: m 8=119 alternateinterior angles

B2: m 8=119

B1: m 8=x 119=x

How can I find x?B1: m 1+90=x remoteexterior angle theoremHow can I find m 1?B2: m 1+150=180

B2: m 1+150=180 -150 -150 m 1=30B1: m 1+90=x

30+90=x 120=x

How can I find x?B1: m 3+47=x remoteexterior angle theoremHow can I find m 1?B2: m 3+21=90

complementary angles

B2: m 3+21=90-21-21

m 3=69B1: m 3+47=x

69+47=x 116=x

How can I find x?B1: m 4=xalternate interior anglesHow can I find the m 4?B2: m 4+125=180consecutive angles

B2: m 4+125=180-125-125

m 4=55

B1: m 4=x 55=x

(Sometimes a very hard lookingproblem can have an easy solution.)


405/553

s1+s2=s37+7>1314>13 truetriangle



s1+s2=s3

21+18>3439>34 truetriangle

s1+s2=s38+9>1717>17 false

no triangle

s1+s2=s345+46>9191>91 falseno triangle


s1+s2=s336+25>6161>61 falseno triangle



s1+s2=s34+7>1111>11 false!no triangle

s1

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