Geometry MPD 1
HW #6 / questions 19-29
8.4
EXERCISES
HOMEWORK
KEY
5 WORKED-OUT SOLUTIONS
on p. WS1 for Exs. 7, 15, and 55
★ 5 STANDARDIZED TEST PRACTICE
Exs. 2, 30, 31, and 62
SKILL PRACTICE
1. VOCABULARY What is another name for an
W
equilateral rectangle?
2.
EXAMPLES
1, 2, and 3
on pp. 534–535
for Exs. 3–25
★ WRITING Do you have enough information to
identify the figure at the right as a rhombus? Explain.
X
Z
Y
RHOMBUSES For any rhombus JKLM, decide whether the statement is
always or sometimes true. Draw a diagram and explain your reasoning.
3. ∠ L > ∠ M
5. }
JK > }
KL
4. ∠ K > ∠ M
6. }
JM > }
KL
7. }
JL > }
KM
8. ∠ JKM > ∠ LKM
RECTANGLES For any rectangle WXYZ, decide whether the statement is
always or sometimes true. Draw a diagram and explain your reasoning.
10. }
WX > }
YZ
9. ∠ W > ∠ X
12. }
WY > }
XZ
}> }
11. WX
XY
13. }
WY ⊥ }
XZ
14. ∠ WXZ > ∠ YXZ
CLASSIFYING Classify the quadrilateral. Explain your reasoning.
15.
16.
17.
1408
408
1408
18. USING PROPERTIES Sketch rhombus STUV. Describe everything you know
about the rhombus.
USING PROPERTIES Name each quadrilateral—parallelogram, rectangle,
rhombus, and square—for which the statement is true.
19. It is equiangular.
20. It is equiangular and equilateral.
21. Its diagonals are perpendicular.
22. Opposite sides are congruent.
23. The diagonals bisect each other.
24. The diagonals bisect opposite angles.
25. ERROR ANALYSIS Quadrilateral PQRS is a rectangle. Describe and correct
the error made in finding the value of x.
P
(7x – 4)°
S
Q
(3x + 14)°
R
7x 2 4 5 3x 1 14
4x 5 18
x 5 4.5
8.4 Properties of Rhombuses, Rectangles, and Squares
537
ALGEBRA Classify the special quadrilateral. Explain your reasoning.
Then find the values of x and y.
26.
27.
B
3y
1048
x8 C
y18
A
2y
P
★
31.
★
2y 1 35
29.
R
E
(3x 1 18)8
F
2y 1 1
(4x 1 7)8
H
S
M
(5x 2 6)8
y13
10
30.
5x 2 9
J
5x8
L
x 1 31
D
28. P
4y 1 5
K
G
SHORT RESPONSE The diagonals of a rhombus are 6 inches and
8 inches. What is the perimeter of the rhombus? Explain.
MULTIPLE CHOICE Rectangle ABCD
is similar to rectangle FGHJ. If AC 5 5,
CD 5 4, and FM 5 5, what is HJ?
A 4
B 5
C 8
D 10
F
A
G
B
M
E
D
J
C
RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that
m ∠ BAC 5 538 and DE 5 8, find the indicated measure.
32. m ∠ DAC
33. m ∠ AED
34. m ∠ ADC
35. DB
36. AE
37. AC
A
B
538
8
E
D
C
RECTANGLE The diagonals of rectangle QRST intersect at P. Given that
m ∠ PTS 5 348 and QS 5 10, find the indicated measure.
38. m ∠ SRT
39. m ∠ QPR
40. QP
41. RP
42. QR
43. RS
P
R
P
348
T
S
SQUARE The diagonals of square LMNP intersect at K. Given that LK 5 1,
find the indicated measure.
44. m ∠ MKN
45. m ∠ LMK
46. m ∠ LPK
47. KN
48. MP
49. LP
L
M
1
K
P
N
COORDINATE GEOMETRY Use the given vertices to graph ~JKLM. Classify
~JKLM and explain your reasoning. Then find the perimeter of ~JKLM.
50. J(24, 2), K(0, 3), L(1, 21), M(23, 22)
538
5 WORKED-OUT SOLUTIONS
on p. WS1
51. J(22, 7), K(7, 2), L(22, 23), M(211, 2)
★ 5 STANDARDIZED
TEST PRACTICE
H