..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
\