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Geometry Unit 2 - Day 1 - Points Lines and Planes Homefun
Use the figure to the right to answer the following questions.
1. Write two other names for
2. Write two lines going through point G.
3. Name a point not on the line
4. Name three collinear points.
5. Name three non collinear points.
6. Are all the points coplanar? Explain.
Use the figure to the right to answer the following questions.
7. Name the three line segments that intersect
at point N.
8. What do plane MPRQ and plane NMP have
in common?
9. Name two coplanar planes (if possible).
10. Name the two planes that share
11. Name three collinear points (if possible).
BG
AD
SN
, , , ,BE BG EB GE EG
, ,AD BE CF
, , ,B C F E, ,
, ,
, ,
B G E
A G D
C G F
, , , , , ,
Various
A B C C D E A F G
Yes
, ,MN PN SN
MP
Not Possible
, plane SNMQ plane SNPR
Not Possible
Draw and label a figure for each situation described.
12. Lines ,m, and j intersecting at P. 13. Plane W that contains line y.
14. Points A, B, C, and D are noncollinear.
15)
a) Camille is correct.
b) Hiroshi is correct.
c) They are both correct.
d) Neither of them are correct.
Geometry Unit 2 - Day 2 - Angle Basics
Name each angle in four ways. Then identify its vertex and its sides.
1. 2. 3.
In the following diagrams, give the total number of angles in the diagram.
4. 5.
Use the diagram to the right to find the following.
6. Name the vertex of โ 2
7. Name the vertex of โ ๐ด๐ท๐น
8. Name two other ways to write โ 1
9. Name the right angle in two different ways.
10. Name an angle that appears to be obtuse.
: , , , 5
: ,
:
Angles ABC CBA C
Sides BC BA
Vertex B
: , , , 8
: ,
:
Angles PMN NMP M
Sides MP MN
Vertex M
: , , , 9
: ,
:
Angles XYZ ZYX Y
Sides YZ YX
Vertex Y
36
E
D
, , ,BEG FEG BEC FEC
3, ,FEA BEA
, ,AEC BFG BFD
11. Excluding straight angles, how many angles are shown in the figure?
A. 7
B. 18
C. 19
D. 21
Mixed Review
Use the diagram to the right for 1 โ 3.
Mixed Review: For 4 โ 5, find the midpoint and length of each segment.
5. 6.
P
plane RST
, , ,
Various
RS PQ RP WS
5 2
5 1,
2 2
d
M
4 13
1,1
d
M
Geometry Unit 2 - Day 3 โ Linear Measure
Directions: Find the Measure of the stated segment.
1. AC = __________ 2. DC = __________
3. BC = __________ 4. EF = __________
5. JI = __________ 6. NO= ____________________
4 10 D F C9 10.5
30
A B C13E F G
25
42
M N O
38
19
14 19.5
17 17
32 19
In the diagram below, ๐ด๐ธ = ๐๐, ๐ด๐ต = ๐, ๐ด๐ต = ๐ต๐ถ, and ๐ถ๐ท = ๐ท๐ธ. Find the following pieces. 7. MP
8. NP 9. NQ
For 10 โ 12, use the diagram, and that ๐จ๐ซ = ๐๐,๐จ๐ฉ = ๐,๐ฉ๐ช = ๐.
10. Find CD
11. Find BD
12. Find AC
13. Suppose that B is in between A and C. If ๐ด๐ถ = 36, which of the following is not a possibility for AB (select all that apply)? a) โ5 b) 1 c) 15.4 d) 29 e) 37
Mixed Review:
Solve the following equations and check it.
14. ๐ฅ2 โ 5๐ฅ โ 14 = 0 15. ๐ฅ2 โ ๐ฅ โ 56 = 0
DCBA
20
15
25
10
19
14
2, 7x x 7, 8x x
Geometry Unit 2 - Day 4 โ Linear Measure Part II
Directions: Use the Segment Addition Postulate to find the value of each variable or segment measure.
1. ๐ฅ = __________ 2. ๐ฅ = __________
3. XY= ___________ 4. LM= ____________
5. Given the diagram for the right, which of the following is true?
a) ๐ฅ = 5
b) ๐ฅ = โ5
c) ๐ด๐ต = 20
d) ๐ต๐ถ = 23
e) None of the above
X Y Z
40
3 5x 4xK L M7
6 4x
5 3x
X Y Z
40
3 5x 4xK L M7
6 4x
5 3x
5 6
20 33
Suppose M is between L and N. ML= 3x + 10, MN= 75 โ 10x, and LN= 50. Find the length of each segment.
7. ML =
8. MN =
9. Given: ,ST SR QR SR Solve for x.
10. Given: ,XY YZ WX XY , find XY
Mixed Review: Determine if the following are true or false.
11. R, S, and T are collinear. 12. There is only one plane that contains all the
points R, S, and Q. 13. Plane A and plane TRS are the same plane. 14. Plane B contains 15. Points R, S, and K make a plane.
Q R
S T
3 6x 2(4 12)x
PH
25
25
6x
114XY
True
True
False
False
False
Geometry Unit 2 - Day 5 - Angle Addition Postulate
Find the following for each example.
1. m ABC __________ 2. m ABD __________ 3. m EBC __________
Use the diagram to the right for the following.
4. 1m ___________
5. m TXU ___________
6. m VXU ___________
7. m RXU ___________ 8. m VXS ___________ 9. m RXV ___________
121m ABC
82
70
50
m RXT
m UXS
m TXV
69 22 142
44
32
18
114 88 132
10. Given: 170m DEA , , โ ๐ท๐ธ๐ถ โ โ ๐ถ๐ธ๐ต. Find m CEB
11. Let ๐ be in the interior of POR . 4m POQ x , 2 2m QOR x , and 26m POR .
Find the value of x, and m QOR (Hint: draw a picture first).
12. Let ๐ be in the interior of โ ๐๐๐. ๐โ ๐๐๐ = 180ยฐ , ๐โ ๐๐๐ = (๐ + 1)ยฐand
๐โ ๐๐๐ = (5๐ โ 13)ยฐ Which of the following are true statements (select all that apply).
a) ๐ =7
2
b) ๐ = 5
c) ๐ = 32
d) ๐โ ๐๐๐ = 33ยฐ
e) ๐โ ๐๐๐ = 6ยฐ
f) ๐โ ๐๐๐ = 147ยฐ
g) ๐โ ๐๐๐ = 12ยฐ
MIXED Review:
Name each angle in four ways. Then identify its vertex and its sides.
13. _____ _____ _____ _____ Sides: _______ _________
Vertex: ________
A
B
C
D
Ex
50
60
60
x
m CEB
8
14
x
m QOR
, , , 8ABC CBA B ,BA BC
B
14. X is between A and C and C is between X and D. If ๐ด๐ = ๐๐ถ, ๐ด๐ท = 42, and ๐ถ๐ท = 16, find the length of AX. Hint: Draw the picture and label the lengths.
13AX
Geometry Unit 2 - Day 6 โ Vertical Bisectors For 1 โ 5, AB is an angle bisector. Find the following.
1. x ____________ 2. m ABD ____________ 3. m DAB ____________
4. m CBA ____________ 5. m ZAB ____________ if ๐โ ๐๐ด๐ = 2๐ โ 4,๐โ ๐ต๐ด๐ = 2๐ โ 36.
For 6 โ 7, ๐ฌ๐ฉโโโโโโ is the angle bisector of โ ๐จ๐ฌ๐ช.
6. Find ๐โ ๐ต๐ธ๐ถ. 7. Find ๐ฅ
a) ๐โ ๐ต๐ธ๐ถ = 18.5ยฐ a) ๐ฅ = 35
b) ๐โ ๐ต๐ธ๐ถ = 19ยฐ b) ๐ฅ = 51.5
c) ๐โ ๐ต๐ธ๐ถ = 38ยฐ c) ๐ฅ = 70.5
d) ๐โ ๐ต๐ธ๐ถ = 71ยฐ d) ๐ฅ = 142
20 90 26
60 32
8. Find the value that would make ๐ด๐ตโโโโ โ an angle bisector of โ ๐ถ๐ด๐ and ๐โ ๐ถ๐ด๐ = 150ยฐ. For 9 โ 12, decide if the following are true or false. If they are false, explain why. 9. Every angle has exactly one angle bisector. 10. You can assume a ray is an angle bisector.
11. If two angles are congruent, then they share an angle bisector. 12. Straight angles cannot have an angle bisector. Mixed Review: Use the diagram for the following
13. Name three collinear points.
14. Name three non-collinear points.
15. Name a point that is coplanar with points B, C and F.
20x
True
False
False
False
, ,
, ,
E H F
F I G
, , , ,
Various
A B E or B C G
G or I
Name: ____________________________
Date: __________ Period:_____________
Geometry Unit 2 - Day 7 โ Segment Bisectors
For 1 โ 2, ๐ด๐ตโโโโ โโ โ is a segment bisector of ๐จ๐ฉฬ ฬ ฬ ฬ . 1. Find x
2. Find ๐ด๐ต
For 3 and 4, ๐ฌ๐ญโกโโโ โ is a segment bisector of ๐บ๐ปฬ ฬ ฬ ฬ . Solve for x.
3. Find x 4. Find ๐๐
5. What value(s) of x would make ๐ถ๐ฬ ฬ ฬ ฬ ฬ a segment bisector of ๐ด๐ตฬ ฬ ฬ ฬ
6. What value of x would make ๐๐ฬ ฬ ฬ ฬ a segment bisector of ๐๐ฬ ฬ ฬ ฬ ฬ
a) ๐ฅ = โ4
b) ๐ฅ = 4
c) ๐ฅ = 7
d) ๐ฅ = 11
6 & 1x x
12AB
8 & 7x x
56US
2 & 6x x
Mixed Review:
7. How many points make a plane (select all that are true)?
a) Just 1 point is needed
b) Any 2 points
c) 3 collinear points
d) 3 non-colinear points
e) 4 non-collinear points
f) 4 collinear points
For 8 โ 10 all use the same diagram.
8. Draw a picture to illustrate the following: K is in between J and M, and L is in
between K and M, and ๐ฝ๐พฬ ฬ ฬ โ ๐พ๐ฟฬ ฬ ฬ ฬ โ ๐ฟ๐ฬ ฬ ฬ ฬ
9. Find JK if ๐ฝ๐ = 21
10. Find MK
11. Find the 67Om PQM , find m MQN 12. How do you label the following ray?
7x
14MK
37m MQN
TS
Geometry Unit 2 - Day 8 โ Putting it All Together
For 1 and 2, assume that Y is in between X and Z. ๐ฟ๐ = ๐๐ โ ๐, ๐๐ = ๐๐ โ ๐, and
๐ฟ๐ = ๐๐.
1. Find ๐
2. Find XY
For 3 โ 4, suppose that M is in between L and N. ๐ด๐ณ = ๐๐ + ๐๐, ๐ด๐ต = ๐๐ โ ๐๐๐, and
๐ณ๐ต = ๐๐.
3. Find ๐ฅ
4. Find ML
For 5 โ 6, use the given information. G is in between A and B, ๐จ๐ฎฬ ฬ ฬ ฬ โ ๐ฎ๐ฉฬ ฬ ฬ ฬ ,
๐จ๐ฎ = ๐๐ โ ๐๐, ๐ฎ๐ฉ = ๐๐ โ ๐, and ๐จ๐ฉ = ๐๐.
5. Find ๐ฅ
6. Find AG
For 7 โ 8, let Q be in the interior of โ ๐ท๐ถ๐น. ๐โ ๐ท๐ถ๐ธ = (๐ + ๐)ยฐ, ๐โ ๐ธ๐ถ๐น = (๐๐ โ ๐)ยฐ, and
๐โ ๐ท๐ถ๐น = ๐๐ยฐ. Find the following.
7. Find ๐ฅ
8. ๐โ ๐๐๐
4.5n
1XY
5x
25ML
6x
12AG
8x
14m QOR
For 10 โ 11, D is in the interior of โ ๐จ๐ฉ๐ช. โ ๐จ๐ฉ๐ช is a right angle, ๐โ ๐จ๐ฉ๐ซ = (๐๐ โ ๐๐)ยฐ, ๐โ ๐ซ๐ฉ๐ช = (๐๐ + ๐๐)ยฐ. Find the following.
9. Find x
10. ๐โ ๐ท๐ต๐ถ
For 11 โ 12, K is between J and L. If ๐ฑ๐ฒ = ๐๐ โ ๐๐, ๐ฒ๐ณ = ๐๐ โ ๐, and ๐ฑ๐ณ = ๐๐. Find the following.
11. JK
12. KL
13. D is in the interior of โ ๐ด๐ต๐ถ. ๐ต๐ทโโโโโโ is an angle bisector of โ ๐ด๐ต๐ถ. ๐โ ๐ด๐ต๐ท = (๐ฅ2 โ 5๐ฅ)ยฐ and
๐โ ๐ท๐ต๐ถ = (5๐ฅ โ 9)ยฐ. Find ๐โ ๐ด๐ต๐ถ.
a) ๐โ ๐ด๐ต๐ถ = 9ยฐ
b) ๐โ ๐ด๐ต๐ถ = 18ยฐ
c) ๐โ ๐ด๐ต๐ถ = 36ยฐ
d) ๐โ ๐ด๐ต๐ถ = 72ยฐ
14. X is in between A and C. C is in between X and D. If ๐ด๐ = ๐๐ถ, ๐ด๐ท = 42, and ๐ถ๐ท = 16.
Which of the following is the length of ๐ด๐?
a) ๐๐ = 11
b) ๐๐ = 12
c) ๐๐ = 13
d) ๐๐ = 14
e) None of the above
5x
10m DBC
12JK
16KL
Geometry Unit 2 - Day 9 - Angle Relationships
Describe the relationship of angles 1 and 2 in as many ways as possible using Supplementary, Complementary, Linear Pair, and/or Adjacent Angles.
1. 2. 3.
4. 5. 6.
For 7 โ 10, use the diagram to the right.
7. Which angle forms a linear pair with AGF ?
8. Name two complementary angles.
9. Name an angle that is supplementary to CGD .
10. Which angle forms a linear pair with BGE ?
Adjacent
Adjacent
Supplementary
Linear Pair
Complementary
None
Adjacent
Supplementary
Linear PairNone
FGD
& CGD EGD
CGA
EGF
11. Assuming that A is supp. to B . 12. Assuming that A is comp. to B .
Fill in the following. Fill in the following.
m A 62 118 3
m B
13. What is the measure of an angle that is supplementary to HIJ if 54m HIJ ?
14. What is the measure of an angle that is complementary to DEF if 74m DEF ?
15. Find the value of x 16. Find the value of x
m A 62 78 3
m B 118 62 117 28 12 87
126
16
22x
40x
Geometry Unit 2 - Day 10 Vertical Angles and Linear Pairs-
Determine โ ๐ and โ ๐ are linear pair, vertical angles, or neither. 1. 2. 3.
Solve for the following variables.
3. 4. 5.
6. Given the diagram to the right, which of the following are true (select all that are
true)?
a) ๐ฅ = 10
b) ๐ฆ = 10
c) ๐ฅ = 16
d) ๐ฆ = 16
e) ๐โ ๐ด๐ธ๐ท = 64ยฐ
f) ๐โ ๐ด๐ธ๐ต = 64ยฐ
g) ๐โ ๐ด๐ธ๐ท = 116ยฐ
h) ๐โ ๐ท๐ธ๐ถ = 116ยฐ
Vertical
AnglesLinear
Pair
neither
123
57
x
y
106
74
x
y
45
30
x
y
7. In the figure ๐บ๐นโโโโ โ โฅ ๐บ๐ปโโโโโโ , ๐โ ๐น๐บ๐ผ = (8๐ฅ)ยฐ, and ๐โ ๐ป๐บ๐ผ = (2๐ฅ โ 20)ยฐ. Find ๐โ ๐น๐บ๐ผ and ๐โ ๐ป๐บ๐ผ.
8. Find the value(s) of x 9. Find the value(s) of y
10. Find the value of the variables.
88
2
m FGI
m HGI
12
10
x
x
1
6
y
y
21
48
y
x
Mixed Review:
11. ๐ธ๐ตโโโโ โ is the angle bisector of โ ๐ด๐ธ๐ถ. What is the value of x?
A. ๐ฅ = 35
B. ๐ฅ = 51.5
C. ๐ฅ = 70.5
D. ๐ฅ = 142
12.
Given the information below, find ๐ต๐ถ.
๐ต is between ๐ด and ๐ถ
๐ด๐ถ = 2๐ฅ + 8
๐ด๐ต = 4๐ฅ โ 16
๐ต๐ถ = 3๐ฅ โ 6
A. ๐ต๐ถ = 6 C. ๐ต๐ถ = 12
B. ๐ต๐ถ = 8 D. ๐ต๐ถ = 20
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