Name.
Geometry Worksheet
Date__
Rectangles. 5quares & Rhombi (6.4)
In rectangle ABeD, AB = 2x
1.
+
3y,
.) (.9.'~+. 3 ~.::.J~)
-3 ( 5 x.- a- ~ = \ 'I )
,
_Period,
_
Be = 5x - 2y, CD = 22, and AD = 17. Find x and y .
i.t.~ +1., ~:.
15"l.
. 10 % -
\ q ox,
u·
_
4~",
\'(,~
5\
s:" \
Aro::::::---,c;,...t::,~-8---:::=o'1B
. _d
= q 5,
5't- J 'if
\1
.~ - .., ,
In the diagram for problems 2-7,QRST is a rectangle and QZRC is a parallelogram.
3. If mLTQC = 70, find mLQZR.
2. If QC = 2x + 1 and TC = 3x - 1,
z
find x.
a x .+-\ = :3~ - \
Q tE-------"'"
{ J. ::. )<. \
(;>
~--------~s
T
4. If mLRCS = 35, find mLRTS.
Q
5. If mLQ~T = mL_TRS,find mLTCQ. Z
z
~----------=::..
T
6. If RT =
X2
5
2y, and CS = 14 - x.
values of x and y. Is QZRC a "special"
_
parallelogram? If so, what kind?'i\-\ ':> a.. t'hom bu..$
7. RZ = 6x, ZQ
and QC = 4x - 6, what is the value of
x?
').
z
y.. z: S?x - \2-
10')(
'2.
'"
tn L G 1 R ~ \ '-\-0 ,
R
- 8)<'H"2
::. 0
Q ~----------,;;;;..
R
l~
-2.') l", - ~) =- 0
\ '" ::. do
)I; Z ~
\
T ~
~::::..J 5
::.
z
i4 -)(
-, ~ -=- \ '+
.,\ )( -=;;t\ \ ~:: -"3 \
~
~,
.3~~
Q:',~~~~~
~'1a'r\::' \2
do
~(p
---------------------~~
Use rectangle STUV for questions 8-11.
c
8. If mLI = 30, mL2 = '75
10. If mL8
+
.
.
9. If mL6 = 57, mL4 =
= 3x
o
3.3 .
= 133, mL2 = lD 1.0
'1
tJ
5.
u0
11. If mL5 = 16, mL3 = _.....:.....'....!.-
12. ABCDis a rhombus. If the perimeter of
ABCD= 68 and BD = 16, find AC.
B', \.
~::\I
7.
\
=-\1
'2-
'f.. -;..
~as
X-=- \5
13. ABCDis a square. If mLDBC =
)(:-4"~ 4S
X -
2-
'1.
&""'A
AC=-.$o \
c
A
Y )(.- 4-5 =-0
(,~.,'-q)()(.+5) =-0
\" )('::q
X ::. -~\
.
4x, find x.
X2 -
0
A
B
D '6
e
"
Use
rhombus ABeD for problems 14-19
d-.8 '.
14. If mLBAF:: 28, mLACD::
5..d.5.
,15. If mLAFB = 16x + 6, x ::
qo
1(0 X -\--\0 :::
\, J- , .
16. If mLACD = 34, mLABC =
\:2...0-' 1.\ 'f..:= qD '
?,o
1..5 "
17. If mLBfC :: 120 - 4x, x::
:.l\
3
18. If mLBAC:: 4x + 6 and mLACD:: 12x -18, x::
4 ~+(.,.~ \ 2 y.. -\ g
19. If mLDCB::
Xl -
~
a~~8~
\
6 and mLDAC:: 5~,+ 9, x::
~
~2-to~-;l"l::0
J.(LbA-c..')= L'DC.£>
~
..
'
\bx-+\~
::.. ~2.-Cc
().-\2.)(y..4-2)=-O
20. ABeD is a square. A8:: 5x + 2y, 21. A contractor is measuring for the foundation of a building that
AD :: 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 \.
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 :: 94
5.,. -i-l
3"- 't
u ft. Is WXYZ a rectangle? If not, which way should stekes E and.f
(~
'.
_, \')
be moved to made WXYZ 'a rectangle?
'
08
£
'a ~ \,
"'J.-,'3- t,,~ - 1't :::.
1..2-
:).. ~v
\\'X
r-
-:.
'X. ~
D
\'
C
not ,ecl-~~~\e 6ec.a.use
dlo.. oVl<l.\.s a:ce t\o+ ~
33
,5 ~a~ -=- \\
3-l
'"~-a~
3
=- ).
'_, F
G'~' :;::::-:------~-
D
T
~~_c401
'--,
\-~=-it
HI-;~~-----~--~
..
..
A
b
22. A8CD is a rectangle. Find the length of each
B'
diagonal if AC:: Z(x - ,3) and BD = X" 5.
~~ -\0
1-1
---85ft----I
+-.5
t)
B
23. ABeD is Q rectangle.
3c
A~,=9 and BD:: 4-
Find each diagonal if
c,
0c":
oc, ~ '+_ c,
,C
\')(- \\J (1C:; Bt> = -I'~;;j,:
Q~-
\....
2_C.
'1.
q c..
:;:-=-O.:.::;(.,;.-._-~1
C.=-3
Given rectangle QRST
"
\ J.C
0
10 5
e
24 .' If RX == QT , find mLTXS.
2~. If mLRQS
= 30° and QS
:: 13, find SR.
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
CD:: 8x - 2y + 2. ,Find x and y.
Find x, SR, and QR.,
%-+
-I:::I~.
5't-+-""'k.-8~11
2. ,
-s
~_ '
. q'J!--:.~'7 B
C
~ -or~::.4"''
(0-;)..
,
,~i-,-
~
I ','
"'~~.3l
gX-;}'t+-2""'~'
~
tI--x.
-,a- -.:.'~:
(
/:
~4J ~
. '3 .
<?
"Z.
'1- -bx+-5'~O
i:«>
5)(~-\)';'O
\.')(.c:.S\;>4
~ R ~ Q ~ -=- \5"
=
X2 -
2x. QR = 4x - 5.
..•
p
o
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
example, if you say the sides are parallel then you need to calculate the slopes.
/_
1-;'f
29. W(5, 6), X(7, 5), Y(9,9), Z(7, 10)
Slope
I \
cpr
Parallelogram:
Rectangle: W
\"1
,:>\Ae-;
\\
5,· Sic\es
l
s\cre..
\\Ii::.. ~
=....L
5 -,
- 2.
-n -;.'3~~~:;
-~
c\t{(..%-
i'\o-
__
z ~""
Z.
store N: 5-« _ ~ _ '
hO-\-.L
z.
\\
\
s\ope
-~
s\O?e.. We ~ ~
5-,
Rhombus:
5.
2:1
~-
7-2-
.
,
l,
y
.
--
Ic-q
-
5-10
W'(-=- 5.q"~
3
.
6\o~ey.=t :;..;::J::u.rcle
I
I
Square: no - v\o~ rho\'Y\ bOS
30. W(-3, -3), X(I, -6), Y(5, -3), Z(1, 0)
Parallelogram: ~es Rectangle:
l')O -
0 ~
p
to'ClS ~ \
Rhombus: ~es - c\w_% ..
Square:
VlO'-
Slc\e~ \\
d es no+...L
L
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.
State 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.
'.
31. E(O, -3), F(-3, 0), G(O, 3), H(3, 0)
Parallelogram:~es-off's;c\e6\l
Rectangle: \tes-
C.CI."S,
Slde51.
S\o~e
Square: ~es-
rec\..~ rhoMbv.s
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
z:
-3-D
0e
\
-= -\
Oi-~
1=-6::
~
\\
=- ::.1 =. \
-0
0- ~ _- 3 _
-
- ~-o
-:::-:;'_\,
.J
G
\-\
)".l.
=-~=-\
;~~
0-3
SIc
32. E(2, 1), F(3, 4), G(7, 2), H(6, -1)
0::
S\opeE" ~ - ~-6
0
bo-\-\-.
E-F
s\orei~6
Rhombus: u.es- d,o..Q. ..L
o
-
1/
s\ofe·E:6-=.-~~=\'H"de.\
'F~
Slope
\1
F
-
0,-6
- .:::;::; ::: 0
f