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Ch 7 Review
1. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
a.
b.
irregular and convex
irregular and concave
2. Which statement is false?
a. All squares are
b.
rectangles.
c.
d.
regular and convex
regular and concave
All rhombuses are rectangles
c. No squares are kitesd.
.
.
All squares are rhombuses
.
3. Which statement is false?
a. Every parallelogram is a rhombus.
b. Every square is a parallelogram.
c.
d.
Every rhombus is a quadrilateral.
Some rhombuses are rectangles.
4. Which type of quadrilateral has no parallel sides?
a. trapezoid
b. rhombus
c.
kite
d.
rectangle
c.
All rectangles are
squares.
d.
All parallelograms
are quadrilaterals.
c.
the diagonals bisect d.
each other
5. Which statement is true?
a. All quadrilaterals
b.
are parallelograms.
All parallelograms
are rectangles.
6. Choose the statement that is NOT ALWAYS true.
For any parallelogram _______.
a. opposite angles are b. the diagonals are
congruent
perpendicular
7. m∠R = 110 and m∠S = 90. Find m∠T. ( not to scale).
a.
b.
90
35
c.
d.
55
70
1
opposite sides are
congruent
Find the value of x. (The figure may not be drawn to scale.)
8.
a.
108
b.
49
c.
74
9. ABCD is a parallelogram. If m∠CDA = 59, then m∠BCD =
a.
118
b.
131
c.
d.
?
51
. The diagram is not to scale.
121
d.
59
10. In kite PQRS, m∠QPO = 50° and m∠QRO = 70°. Find m∠PSR.
a.
b.
m∠PSR = 60°
m∠PSR = 90°
c.
d.
m∠PSR = 100°
m∠PSR = 120°
11. For the parallelogram, if m∠2 = 3x − 30 and m∠4 = 2x − 8, find m∠3. The diagram is not to scale.
a.
b.
22
36
c.
d.
154
144
2
12. The sum of the measures of the interior angles of a convex quadrilateral is _____.
a. 540°
b. 180°
c. 360°
d. 270°
13. Which description does NOT guarantee that a quadrilateral is a kite?
a. perpendicular diagonals
c. one diagonal bisects opposite angles
and the other diagonal does not
b. perpendicular diagonals, exactly one of which d. two distinct pairs of congruent adjacent sides
bisects the other
14. Consecutive angles in a parallelogram are always _.
a. supplementary angles
c.
b. congruent angles
d.
complementary angles
vertical angles
15. The diagonals of a parallelogram always ____.
a. are congruent
b. bisect each other
are perpendicular
are parallel
c.
d.
16. Which statement is false?
a. If a quadrilateral is a square, then it is not a kite.
b. Some parallelograms are rhombuses.
c. All parallelograms are quadrilaterals.
d. If a quadrilateral is a rectangle, then it is a kite.
17. For the trapezoid find the length of the midsegment.
a.
58
b.
25
c.
30
d.
29
18. Use slope or the Distance Formula to determine the most precise name for the figure: A(–1, –4), B(1, –1), C(4, 1),
D(2, –2).
rhombus
a.
b.
square
c.
19. Which statement is NOT always true of a rhombus?
a. The diagonals are perpendicular to each
c.
other.
b. The sum of the diagonals is less than the
d.
perimeter.
20. Choose the statement that is NOT always true.
For an isosceles trapezoid _______.
a. the diagonals are perpendicular
b. the base angles are congruent
c.
d.
kite
d.
trapezoid
The diagonals bisect each other.
Each diagonal is longer than at least one side.
the diagonals are congruent
the legs are congruent
3
21. Find AM in the parallelogram if PN =11 and AO = 6. The diagram is not to scale.
a.
12
b.
5.5
c.
6
c.
d.
RS = 16
RS = 24
c.
d.
All rectangles are quadrilaterals.
All quadrilaterals are squares.
d.
11
22. Find RS.
a.
b.
RS = 20
RS = 18
23. Which statement is true?
a. All rectangles are squares.
b. All quadrilaterals are rectangles.
24. For parallelogram PQLM below, if m∠PML = 83°, then m∠PQL =______ .
a.
b.
c.
d.
m∠PQM
83°
97°
m∠QLM
4
25. If ON = 6x − 6, LM = 5x + 2, NM = x + 5, and OL = 3y + 7, find the values of x and y given that LMNO is a
parallelogram.
1
1
;y =
4
2
a.
x = 4; y = 2
c.
x =
b.
x = 8; y =
1
2
d.
x = 8; y = 2
26. Find the measure of each interior angle of a regular 15-gon.
a. 168°
c. 204°
b. 156°
d. 132°
27. Find the measure of each exterior angle of a regular octagon.
a. 45°
c. 60°
b. 30°
d. 22.5°
28. Find the values of the variables in the parallelogram. The diagram is not to scale.
a.
b.
x = 25, y = 52, z = 103
x = 52, y = 25, z = 103
c.
d.
x = 25, y = 52, z = 128
x = 52, y = 52, z = 128
29. Given isosceles trapezoid ABCD with AB ≅ CD, BY = 10.3 , and AC = 17.2. Find YD.
a.
b.
YD = 17.2
YD = 8.6
c.
d.
YD = 10.3
YD = 6.9
5
30. Judging by appearance, classify the figure in as many ways as possible.
a.
b.
rectangle, square, quadrilateral,
parallelogram, rhombus
rectangle, square, parallelogram
c.
rhombus, trapezoid, quadrilateral, square
d.
square, rectangle, quadrilateral
31. Which description does NOT guarantee that a quadrilateral is a parallelogram?
a. a quadrilateral with both pairs of opposite sides congruent
b. a quadrilateral with the diagonals bisecting each other
c. a quadrilateral with consecutive angles supplementary
d. quadrilateral with two opposite sides parallel
32. The sum of the measures of the interior angles of a polygon is 1440°. Classify the polygon by the number of sides.
a. dodecagon
c. decagon
b. 11-gon
d. octagon
33. Find the value of x.
a.
b.
47
110
c.
d.
68
112
34. A convex pentagon has exterior angles of 83°, 83°, 26°, and 46°. What is the measure of an exterior angle at the
fifth vertex?
a. 58°
b. 122°
c.
d.
131°
49°
6
2
35. Find the values of x and y in the parallelogram when AB = x − 18, CD = 7x, m∠D = (5y + 31)°, m∠B = 96°.
a.
b.
x = −2, y = 13
x = 9, y = 10.6
c.
d.
x = 9 or –2, y = 13
x = 9 , y = 13
36. Find the coordinates of the intersection of the diagonals of
and G ÊÁË −6,−4 ˆ˜¯ .
a. ÊÁ −3,0 ˆ˜
Ë
¯
Ê
Á
˜ˆ
b.
Ë −1,0.5 ¯
37. Three vertices of
a.
b.
ÊÁ −1,5 ˆ˜
Ë
¯
ÊÁ −1,5 ˆ˜
Ë
¯
c.
d.
DEFG with vertices D ÊÁË −2,−3 ˆ˜¯ , E ÊÁË 0,4 ˆ˜¯ , F ÊÁË −4,3 ˆ˜¯ ,
ÊÁ −4,−3.5 ˆ˜
Ë
¯
ÁÊ 1,−3 ˜ˆ
Ë
¯
DEFG are D ÁÊË 2,3 ˜ˆ¯ ,E ÁÊË −5,2 ˜ˆ¯ ,G ÁÊË 6,6 ˜ˆ¯ . Find the coordinates of F .
c. ÊÁ −8,5 ˆ˜
Ë
¯
d. ÊÁ −12,1 ˆ˜
Ë
¯
38. For what values of x and y is quadrilateral ABCD a parallelogram?
a.
b.
x = 12, y = 3
x = 6, y = 12
c.
d.
x = 6, y = 3
x = 74, y = 105
39. Find the lengths of the diagonals of rectangle QRST when QS = 20x − 5 and RT = 14x + 7 .
a. 35
c. 70
b. 99.7
d. 17.5
7
Find the measures of the numbered angles in rhombus QRST.
40.
a.
b.
c.
d.
m∠1 = 90°, m∠2 = 31°, m∠3 = 31°, m∠4 = 31°
m∠1 = 90°, m∠2 = 31°, m∠3 = 59°, m∠4 = 59°
m∠1 = 118°, m∠2 = 31°, m∠3 = 31°, m∠4 = 31°
m∠1 = 31°, m∠2 = 74.5°, m∠3 = 74.5°, m∠4 = 74.5°
41. Find the length of the midsegment of the trapezoid.
a.
b.
29
47.5
c.
d.
8
39.5
c.
d.
8
5
42. Find AB.
a.
b.
21.5
11
8
43. A scenic overlook which extends over a ravine is shaped like a kite.
Find m∠X .
a. 40°
b. 112°
c.
d.
104°
208°
44. The watch face shown is shaped like a regular decagon. Find the measure of each interior angle of the watch face.
Then find the measure of each exterior angle.
a.
b.
interior: 144°; exterior: 36°
interior: 36°; exterior: 144°
c.
d.
interior: 18°; exterior: 162°
interior: 162°; exterior: 18°
Classify the special quadrilateral.
45.
a.
b.
c.
rhombus
rectangle
square
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46.
a.
b.
c.
rhombus
rectangle
square
a.
b.
c.
rhombus
rectangle
square
a.
b.
c.
rhombus
rectangle
square
47.
48.
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
49. Quadrilateral ABCD is a kite. What conditions must be true?
a. no parallel sides
c. diagonals are perpendicular
b. opposite sides are congruent
d. 2 pair congruent sides
10
Matching: Put the LETTER for the correct answer in the blank ____at the end of the question.
Match each vocabulary term with its definition.
a. concave
b. convex
c. diagonal
d. regular polygon
e.
f.
g.
h.
side of a polygon
vertex of a polygon
quadrilateral
trapezoid
50. the common endpoint of two sides of the polygon____
51. a segment that connects any two nonconsecutive vertices of a polygon ____
52. a polygon in which no diagonal contains points in the exterior of the polygon____
53. a polygon that is both equilateral and equiangular____
54. a polygon in which a diagonal can be drawn such that part of the diagonal contains points in the exterior of the polygon ____
Short Answer
55. In what type of trapezoid are the base angles congruent?
Open-ended:
56. Using the drawing and the triangle sum theorem, explain why the sum of the measures of the interior angles of a
pentagon is 540° (make triangles from one vertex).
57. One side of a kite is 3 cm less than 5 times the length of another. If the perimeter is 90 cm, find the length of each
side of the kite.
58. Consider the statement, "If a parallelogram is a square, then it is a rhombus."
A. Decide whether it is true or false.
B. Write the converse.
C. Decide whether the converse is true or false.
11
59. Refer to the figure below.
Given: UVWX is a parallelogram, m∠WXV = 17°, m∠WVX = 29°, XW = 41, UX = 24, UY = 15
A. Find m∠WVU.
B. Find WV.
C. Find m∠XUV.
D. Find UW.
60. If the diagonals of a parallelogram are equal in length, then the parallelogram is also what type of figure?
61. A regular pentagon has five congruent interior angles. What is the measure of each angle?
62. Find the number of sides of a regular polygon with each interior angle equal to 135°.
63. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure?
64. What is the measure of each interior angle in a regular octagon?
True or False:
65. If a quadrilateral is a parallelogram, then opposite angles are equal in measure.
66. If a quadrilateral is a parallelogram, then consecutive angles are supplementary.
67. All squares are rhombuses.
68. For any rhombus ABCD, is it always or sometimes true that AC ≅ BD ? Explain your reasoning.
69. For any rhombus EFGH, is it always or sometimes true that ∠E ≅ ∠F ? Explain your reasoning.
70. For any rectangle EFGH, is it always or sometimes true that EH ≅ GH ? Explain your reasoning.
71. For any rectangle ABCD, is it always or sometimes true that AB ≅ CD? Explain your reasoning.
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PROOFS
Write a two-column proof.
72. Given LMNO is a parallelogram.
Prove
LMO ≅
NOM
73. Given ABCD and AEFG are parallelograms.
Prove ∠C ≅ ∠F
74. Given ABCD and DEFG are parallelograms.
Prove ∠B ≅ ∠F
13
ID: A
Ch 7 Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
B
B
A
C
D
B
D
D
C
A
D
C
A
A
B
D
D
A
D
A
C
B
C
B
D
B
A
A
D
A
D
C
A
B
D
A
B
C
A
B
A
D
C
1
ID: A
44.
45.
46.
47.
48.
A
B
C
A
B
MULTIPLE RESPONSE
49. A, C, D
MATCHING
50.
51.
52.
53.
54.
F
C
B
D
A
SHORT ANSWER
55. an isosceles trapezoid
56. Sample answer: By drawing all the diagonals possible from one vertex, the pentagon is divided into 3 triangles.
Since the sum of the angles of each triangle is 180°, the sum of the angles of the pentagon is 3 • 180°, or 540°.
57. 8 cm, 37 cm
58. A. True.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
B. If a parallelogram is a rhombus, then it is a square.
C. False.
A. 46° B. 24 C. 134° D. 30
A rectangle
108°
8
A rhombus
135°
True
True
True
sometimes; The diagonals are congruent only when the rhombus is also a square.
sometimes; Consecutive angles are congruent only when the rhombus is also a square.
sometimes; The adjacent sides are congruent only when the rectangle is a square.
2
ID: A
71. always; By the definition of a rectangle, opposite sides are congruent.
OTHER
72.
STATEMENTS
1. LMNO is a parallelogram.
2. LO ≅ NM, LM ≅ ON
3. ∠L ≅ ∠N
4.
LMO ≅
NOM
REASONS
1. Given
2. Parallelogram Opposite Sides Theorem
3. Parallelogram Opposite Angles Theorem
4. SAS Congruence Theorem
73.
STATEMENTS
1. ABCD and AEFG are parallelograms.
2. ∠C ≅ ∠A, ∠A ≅ ∠F
3. ∠C ≅ ∠F
REASONS
1. Given
2. Parallelogram Opposite Angles Theorem
3. Transitive Property of Congruence
STATEMENTS
1. ABCD and DEFG are parallelograms.
2. ∠B ≅ ∠D, ∠D ≅ ∠F
3. ∠B ≅ ∠F
REASONS
1. Given
2. Parallelogram Opposite Angles Theorem
3. Transitive Property of Congruence
74.
3