..Gc.ometry- GTlHonorsChapter 6 Review - Quadrilaterals

Name --~---------------------------Date__ -"--_----.;;:;.. Period _

!Find each of the fonowmg values.

GRAM~ hi 1-4Use parallelogram or pro ems .50 1. GA = 3x - 10 and ;J ('JC:t 20)-= ~)<-IO

~AGP = x + 20. Find x. d.'I(.-+~o= ~'l(-IO

50 z: "I-,~~ P 23

G 37 MI

I 5i 2. mLGMR = 37° and mLAMG = 95°, 105 3. mLRGM = 75°, find mLGMAfind mLGRM. q 5 1&0

-~., - ,~- tOS5~

x= ll. 4. RA = 2x + y, GR = 3x - y, find x and y

y= \~ l.~+,&~~, "L ::: \ 2 ~'"' + ~ ~37

3'i - '4 -:.~~ \!-::.\?> -.3 ~-d?> =- '& 5X-=-<.oO-. 5 ~ ~ tQO X=-I 2-

L d. 'X, + ( 3 -x. -.;2 ~);:. 3 f

Use rectan Ie RECT for robJems 5-8.

~5. IfTA = 3x - 7 and AC = 2x + 2, find x.

.3 'X -7 -:.;t)( + :L

x=9

R E~~~--------~--

T

__ -12 7. IfRT = 2x + 5 and EC = 4x - 11,find x.

~x+.s~l\~-\l

\~::~)(.

8'::)(

~ (, 6. IfmL2 = 33°, find mLII.

',lD 8. If mz.l = x2 - 4 and mL8 = x + 52, find x.~'2. 5~

"2-X - ~+ x, -tSOl ::90

~X -+X+-'t8.=C(ox2.1- x-'t2 = 0

("1"')("-(,,) =0~-1 'l( =

Use rhombus RHOM for roblems 9-11.M R------..---..x= ~ 9.lfMO=24,MR=4x+2y+2,andRH=5x-¥+I4,

y= 5 find x and y- Ii ~.f- aO + 2;. ~'f

5" ~ - '6 '"~''4':.~"\-'t J ,..~1-:''l. "i.

Llsl- '\ ':..I~10.,. -l ~aD

5)(-\(:)~'3-'--\)( +- ~(5~ -10): 2"2...Lt)(+-\O)(.-2c> =22..

----' -11. lfmL7 = 39°, find mL2.10_ If RO = 24 and:MH = 10, find MR.--It....o..oll'---

TR =, 2. 1'V\T=5'1 'a- 26 -'-\2. ::..~

uare SQUA for roblems 12-14.12:--IfAU-=-x'"+ 2 and--SA =3x=' ~~liria«=:....•.......-..-'-

7-'/.. t"~;S )t.-4

.,."a._5)(."'""~ 0(x-2.')t,,--3"':> ':6

----'~-13 _ If mLARS = 6x, find x.Io~=-qo

~ e, \5

_ ~14. mLQAU = 3x - 12, find x.3)( - \:2 :: 1+5 qo+ ~y.-~~ -=-Hr

wl-~,\-:.qo3~;:,.s7 (,'#.7-\\,,\

)\,::.,q ~::.\tt

Use trapezoid TUVW with median XY for problems IS-17.

~t.. IS. IDLV

T ~ -.1"1._ U

104

~~4 16.TU=lS,WV=33,findXY. 15+a3'?> =l\~2,..

w

~17. TU=x-12,XY=x+ IS, WV=3x-8, find x.

~ -1'1 +- 3l<o-_8 _______ - 'f.. or \5

, "'"-'i~ -l..~ ':..,_,~~ 3C>

~~. ':..50 -

v

Use isosceles trapezoid TRAP for problems 18-20.

~118. mLl 1q Iso -m-L.-6=-34

2

~ ~ 't_J 9. mL' '1 (0 ~ - 1'1 .3 mL.7=79°~-____~...,_ 20. mL3 I '-t ~ ,,3 '1 p~------------------~--~~AIn problems 21-23, if there is enough information to state that the quadrilate:al is a ~arallelogram give thereason. Write none if there is not enough information to state that the quadrilateral is a parallelogram. ,

A B21. E is the midpoint of AC and BDd\o..~oY\~\~ b\~e.c.~ eo..c,hothe~~ 0

22. L2 ~ L6 and L3 ~ L7none )on\~ 0"( (>0.\( o~ off side, \\ . D

23. L8 ~ L 4 and AD == BCOht pa\~ 0rr ~iQe~ ~ O-N\cl ,( -? 1-:1

24. The coordinates of the vertices of quadrilateral ABCD are A(-4, -2), B(-l, 3), C(4, 0), and D(l, -5).Determine whether the quadrilateral is a parallelogram, a rectangle, a rhombus, or a square. List allthat apply and, explain why you are listing the ones that you are. SHOW WORK! (A graph is not l)

.s-: ~ sufficient.) , ~ __ --;.D

m~ ~ 5} mAt, ~ - ~

In oc .•. ~. ~ '" e D'" ~'t ~ .1.~ M> ~ - ~ '\/\" 1. ?Q,,(,O--\\C!\o~ro..~ (oft> s\d@~ H) b . '. C

rec.\-ct'J8\e, ("?Q.ro..\\e\o~-("o..YV\ vJ~~ o..G\~Sides j.')1V\~e. "':- -1.. " y\-ombus '( l-] (.0\-\-'" .l.. d'o..%o\'\o..\.s

'j <5<}ua.ye, l~04 \'"ec:\o.",~\e ~ fhoMbus)

25. The coordinates of the vertices of quadrilateral PQRS are P(4, 4), Q(l, 2), R(2, -2), and S(5, 0).Determine whether ~he quadrilateral is a parallelogram, a rectangle, a rhombus, or a square. List allthat apply and explain why you are listing the ones that you are. SHOW WORK! (A graph is notsufficient.)

m (Jo ~ ~ ~ m~::.?> 1. ~o~J.,'( VV\ QS=- J. ~m~~ '2. , .

~'no\"· .L_ L,~ ~ ~-q 1, V~Q(t~-"f~

P R::. fi"L +1o"L:: ~.

QS =- ~z~ ,'L z: ~ 2..0

,~y-o..\\e \~fo.~(o{'f s\de~ \\)

red (); ,'<ts-\ e. - vvo.aA: I. ·S\ &.eS \1\0+ .l.-

'f'nom os - Y') 0\ o....ca V) a+- .l...

sc:uJo.. e - V\ 0 r(V\ r ....e...(.,y ~ ..,~omr;

PQ::.~;; (;3,a~ -= it t~~~=- ~ \ f----~------~--------------

~I\¥l \. ~_

\ \ vJ"" " .. \ \"" .., "'--\;).. \

\ V~·\ql ~ ~~

27. Find the coordinates of the 3 p~ssible points for the missing vertex:\ a parallelogram iftTrr1e of thevertices aret(-2, -1)~-1, 3), an~4, 1). J~

00\"'" a, ~-- -So\", - ".3 "1..-8-'" - ~ :..~-- "

~~ 2. z..

<. ~.-~}(-~~ \)

l5.5)

. .'-

..

•..

' ...•.....•..

28. Given ABeD is a kite and mLBCD=50°mL2=40°ED=6

find mL8= 50.mLADC= loS-BD=--l..l-

•• lA+b+C~~~

29. 8ABC has midpoints D, E, and F. If the perimeter of A.,..~:'. ~~ ....,

~DEF is 23, then find the perimeter of 8ABC.

Find: mL1 = I _~ \20-,

mL2=~

mL3 = '2.'0

mL4~~

30. KITE is a kite. M, N, 0, and P are midpoints.mLKMN=30mLKIT = 100

T

~31. OE is an isosceles trapezoid. T, R, A, and P are midpoints10 = 12 .mLRJT = 75° and mLSRA = 40°

Find: mL1= 3SmL2= 10

~6.mL3=

RA= (p

AP=(p

E

i

\

(Of-C)

E.c.,o)

( -a,o)

@ G~"eYl : Sq.-va.re FG, H-.l.""Prove: F lot .L G .L

\h e €. \o{' e o~ \=-\-\ -=-

The ~tope 0+ (,"1 ':.

F \4- .1 & 1. b e c, a. \J Se,

-\

co (0.,0)(0,'0')

4e.= VCl"Z..+-'o~

B D= ~ b'+n..'" -