Geometry WorksheetRectangles. 5quares & Rhombi (6.4)

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Date__ _Period, _

1. In rectangle ABeD, AB= 2x + 3y, Be = 5x - 2y, CD= 22, and AD= 17. Find x and y ..) (.9.'~+.3 ~.::.J~) i.t.~ +1., ~:. 4~", \'(,~ s:" \ Aro::::::---,c;,...t::,~-8---:::=o'1B

-3 ( 5 x.- a- ~ = \ 'I ) 15"l. . 10% - 5 \ . _ d \1 5't-J 'if, u· \ q ox, = q 5, .~ - .., ,

In the diagram for problems 2-7,QRST is a rectangle and QZRC is a parallelogram.

z2. If QC = 2x + 1and TC = 3x - 1,

find x. (;>

a x .+-\ = :3~ - \ Q tE-------"'" R tn L G 1 R ~ \ '-\-0 ,{ J. ::. )<. \

T ~--------~s

3. If mLTQC = 70, find mLQZR.

4. If mLRCS = 35, find mLRTS. z 5. If mLQ~T = mL_TRS,find mLTCQ. Z

Q ~----------=::..

T 56. If RT = X2 and QC = 4x - 6, what is the value ofx?

').

y.. z: S?x - \2-'2.

'" - 8)<'H"2 ::.0 Q ~----------,;;;;.. R

l~-2.') l", - ~) =- 0\ '" ::. do )I; Z ~ \ T ~ ~::::..J 5

z

Use rectangle STUV for questions 8-11.c

8. If mLI = 30, mL2 = '75o

9. If mL6 = 57, mL4 = 3.3 .10. If mL8 = 133, mL2 = lD 1.0 tJ 5 .

'1 u 011. If mL5 = 16, mL3 = _.....:.....'....!.-

7. RZ = 6x, ZQ = 3x + 2y, and CS = 14 - x.values of x and y. Is QZRC a "special" _parallelogram? If so, what kind?'i\-\ ':> a.. t'hom bu..$10')( ::. i4 -)( z

. ~ ~,-, ~ -=- \ '+ .,- .3~~\ )( -=;;t\ \ ~:: -"3 \ Q:',~~~~~

~'1a'r\::'\2. do ~(p

---------------------~~

12. ABCDis a rhombus. If the perimeter ofABCD= 68 and BD= 16, find AC. B', \.

~::\I \ AC=-.$o \

A7. '1. 2-

&""'A =-\1'2-'f.. -;.. ~as

X-=- \5

13. ABCDis a square. If mLDBC = X2 - 4x, find x.

)(:-4"~ 4S A0.BX - Y )(.- 4-5 =-0

(,~.,'-q)()(.+5)=-0 D '6 e

\" )('::q X ::. -~\

c

"

Use rhombus ABeD for problems 14-19

14. If mLBAF:: 28, mLACD:: d-.8 '.,15. If mLAFB = 16x + 6, x :: 5..d.5. 1(0 X -\--\0 ::: qo

16. If mLACD = 34, mLABC= \, J- , .17. If mLBfC :: 120 - 4x, x:: 1..5 "

\:2...0-' 1.\ 'f..:= qD '?,o :.l\ ~

18. If mLBAC:: 4x + 6 and mLACD:: 12x -18, x:: 34 ~+(.,.~ \2 y.. -\ g

a~~8~ \19. If mLDCB:: Xl - 6 and mLDAC:: 5~,+9, x:: ~

J.(LbA-c..')= L'DC.£> ~2-to~-;l"l::0~ .. '

\bx-+\~ ::.. ~2.-Cc ().-\2.)(y..4-2)=-O20. ABeD is a square. A8:: 5x + 2y, 21. A contractor is measuring for the foundation of a building thatAD :: 3x ~d Be :: 11. Find x and is to be 85 ft by 40 ft. Stakes and string are placed as shown.y. , ~('Y'1-- J \. 08 The oetside corners of the bund;ng will be at the points where the£ i : ',:, ' strings cross. He then measures and finds WY :: 93 ft and XZ :: 945.,. -i-l 'a ~ \, 3"- 't u ft. Is WXYZ a rectangle? If not, which way should stekes E and.f

(~ '. _, \') be moved to made WXYZ 'a rectangle? ':).. ~v "'J.-,'3- -

t,,~ - 1't :::.1..2- D \' C not ,ecl-~~~\e 6ec.a.use 1-1---85ft----Idlo..3oVl<l.\.s a:ce t\o+ ~ '_, F

G'~' :;::::-:------~- D T

HI-;~~-----~--~..~~_c401..'--,

\\'X -:. 33

r 'X. ~ 3-l-,5~a~ -=- \\

'"~-a~\-~=-it

A B23. ABeD is Q rectangle. Find each diagonal if

3cA~,=9 and BD:: 4- c, 0c": Q~- q c..oc, ~ '+_ c, \....2_C. :;:-=-O.:.::;(.,;.-._-~1'1. C.=-3

22. A8CD is a rectangle. Find the length of eachdiagonal if AC:: Z(x - ,3) and BD= X" 5. bB'

~~ -\0 =- ). +-.5 t) ,C

\')(- \\J (1C:; Bt> = -I'~;;j,:Given rectangle QRST" 0\ J.C 24 .' If RX == QT , find mLTXS.

10 e 5 2~. If mLRQS = 30° and QS :: 13, find SR.

(0-;).. 2~. If mLQST e 45° and QT = 6.2, find QR.2.7. Given rhombus ASCD.AB:: 5x .•y - 1. 8C :: 18, 28. Given square PQRS, SR = X2 - 2x. QR = 4x - 5.CD:: 8x - 2y + 2. ,Find x and y. Find x, SR, and QR., ..•

~

%-+ -I:::I~. 5't-+-""'k.-8~11 2. , -s p o~_ ' . q'J!--:.~'7 B C ~ -or~::.4"'- '

, ~i-,- I ',' "Z., "'~~.3l /: '1- -bx+-5'~OgX-;}'t+-2""'~' ( ~4J ~ i:«> 5)(~-\)';'O

~ . '3 . <? \.')(.c:.S\;>4tI--x. -,a- -.:.'~: ~ R ~ Q ~ -=- \5"

Determine whether WXYZ is a parallelogram, a rectangle, a rhombus, or a square for each set of vertices.State yes or no for each and explain why or why not. Show work to support the explanations. For 1-;'fexample, if you say the sides are parallel then you need to calculate the slopes. / _ l,29. W(5, 6), X(7, 5), Y(9,9), Z(7, 10) Slope \\Ii::.. ~ =....L 5 . z. y

I \ 5 -, - 2. \\ .-- Ic-q 3

Parallelogram: cpr ,:>\Ae-; \\ s\cre.. -n -;.'3~~~:; -~ __ \ s\ope W'(-=- 5.q"~-~ . - 5-10 . f

Rectangle: W \"1 5,· Sic\es l s\O?e.. We ~ ~ z ~"" 2:1 6\o~ey.=t :;..;::J::u.rcle5-, Z. ,I

Rhombus: i'\o- c\t{(..%- hO-\-.L store N: 5-« _ ~ _ ' I~- 7-2-

Square: no - v\o~ rho\'Y\ bOS

30. W(-3, -3), X(I, -6), Y(5, -3), Z(1, 0)

Parallelogram: ~es - 0 ~ p Slc\e~ \\

Rectangle: l')O - to'ClS ~ \ d es no+...L

Rhombus: ~es - c\w_% .. L

Square: VlO'- n,o+ r e c\- a.V\S \e

Determine whether EFGH is a para.llelogram, a rectangle, a rhombus, or a square for each set of veEtices. FState yes or no for each and explcin why or why not. Show work to support the explanations. Foro,example, if you say the sides are parallel then you need to calculate the slopes. '.

- -3-D G31. E(O, -3), F(-3, 0), G(O,3), H(3, 0) S\o~e E-F 0:: Oi-~ -= -\ ~ \\ \-\

Parallelogram:~es-off's;c\e6\l s\orei~6 z: ;~~ =-~=-\ )".l. s\ofe·E:6-=.-~~=\'H"de.\

Rectangle: \tes- C.CI."S, Slde51. S\opeE" ~ - ~-6 =- ::.1=. \ 1/ 'F~ - 0,-60-3 -0 Slope - .:::;::; ::: 0

\ 1Rhombus: u.es- d,o..Q. ..L SIc 0e 1=-6:: 0- ~ _- 3 _o 0 \ - -:::-:;'_\,- ~-o .J

Square: ~es- bo-\-\-. rec\..~ rhoMbv.s

32. E(2, 1), F(3, 4), G(7, 2), H(6, -1)

Parallelogram: ~es'-0f'f S\des \\

Rectangle: Y\O - Con~', SI'c.\es ¥lOt-.l

Rhombus: no·- dfo...fr i'\o-t- .J.

square: no ~ neA re.c\-o. \"\~\e:.0'- '('hom buS