Name: Class: Date: Practice Exam II - Chapters 3 & 4
Indicate whether the statement is true or false.
1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square.
a. True
b. False
2. If M and N are midpoints of sides a. True
b. False
and of , then .
3. The reason “Identity,” which is used to state that a line segment or angle is congruent to itself, is also known as the
Reflexive Property of Congruence.
a. True
b. False
4. The diagonals of any rhombus are perpendicular.
a. True
b. False
5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.
a. True
b. False
6. The perimeter P of an isosceles triangle with a leg of length a and base of length b is
given by .
a. True
b. False
7. If the midpoints of the sides of .
a. True
b. False
are joined to form , then the perimeter of will be twice that of 8. The reason for the congruence of two triangles due to the congruence of two pairs of angles and their included pair of
sides is represented by AAS.
a. True
b. False
9. If a. True
b. False
in , then .
10. The method CPCTC can be used to prove that two triangles are congruent.
a. True
b. False
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
11. In a. True
b. False
, and are supplementary.
12. To construct the midpoint of the horizontal line segment , begin by marking off arcs of equal length from points A
and B so that the arcs intersect both above and below .
a. True
b. False
13. If a. True
b. False
and 14. Having proved that a. True
b. False
, then .
by SSS, we can then state that Copyright Cengage Learning. Powered by Cognero.
.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
15. If a. True
b. False
and in quadrilateral ABCD, then ABCD is an isosceles trapezoid.
16. The bisector of one angle of a triangle always separates the triangle into two smaller and congruent triangles.
a. True
b. False
17. When the midpoints of the sides of a quadrilateral are joined in order, the quadrilateral formed is always a square.
a. True
b. False
18. Given that point P is the midpoint of both a. True
b. False
19. In the Pythagorean Theorem (where triangle.
a. True
b. False
20. If sides a. True
b. False
and and , it follows that .
), the number c represents the length of the hypotenuse of a right
of quadrilateral MNPQ are congruent and also parallel, then MNPQ is a parallelogram.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
Indicate the answer choice that best completes the statement or answers the question.
21. In , M and N are the midpoints of a. b. c. d. None of These
22. For a. c. , and as shown. Then:
is an exterior angle. Which of the following must be true?
b. d. 23. Two of the angles of a triangle have measures of 50° and 60°. Which number cannot be the measure of an exterior
angle of this triangle?
a. 100°
b. 110°
c. 120°
d. 130°
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
24. In isosceles triangle RST, is 36, find the value of x.
a. x = 5.5
b. x = 6
c. x = 6.5
d. None of These
. If , 25. If D is the midpoint of , what name is given to a. angle-bisector
b. median
c. altitude
d. hypotenuse
, and the perimeter of in relation to ?
26. If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus?
a. 13 cm
b. 34 cm
c. 52 cm
d. 68 cm
27. The midpoints of the sides of rhombus ABCD are joined in order to form quadrilateral MNPQ. Being as specific as
possible, what type of quadrilateral is MNPQ?
a. parallelogram
b. rectangle
c. square
d. rhombus
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
28. is an altitude for a. 3
b. 3.5
c. 4
d. None of These
29. Given that a. ASA
b. SAS
c. AAA
d. SSS
. If RV = 5, RS = 7, and WT = 4, find the length of altitude and , which method establishes that .
?
30. Both pairs of opposite sides of quadrilateral WXYZ are congruent. Being as specific as possible, what type of
quadrilateral is WXYZ?
a. parallelogram
b. rectangle
c. square
d. rhombus
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
31. In a. b. , . Which statement is true?
is an altitude of .
is an altitude of .
c. is the longest side of .
d. The 3 angle-bisectors meet in the exterior of 32. In a. c. , it follows that
and include b. and and d. and include .
include include 33. In order to justify the construction of the angle-bisector which method?
a. SAS
b. ASA
c. SSS
d. HL
34. In a. 77°
c. 116°
, m is 26° larger than m
b. 103°
d. 126°
. Find m
of , we verify that two triangles are congruent by
.
35. For the angle-measure indicated, which angle cannot be constructed?
a. 22.5°
b. 30°
c. 40°
d. 45°
36. In , m
and m
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. Find the value of x.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
37. In the figure, the perpendicular-bisector of 38. Given kite ABCD with and and , what other relationship exists?
39. In , diagonals 40. What part of and . If and , find WV.
, the diagonals (if drawn) would be perpendicular. For diagonals intersect at point T. If MN = 12.5, NP = 8.7, and QN = 14.6, find QT.
is included by and ?
41. In addition to being congruent, how are the diagonals of a square related?
42. Where , and . Find .
43. When the midpoints of the sides of a square RSTV are joined in order, quadrilateral MNPQ is formed. Being as
specific as possible, what type of quadrilateral is MNPQ?
44. Just as SSS, SAS, ASA, AAS, and HL are methods for proving that triangles are congruent, use three letters to state
two methods that are not valid.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
45. In isosceles trapezoid HJKL, . Suppose that points M, N, P, and Q are the midpoints of the sides and respectively. If the length of diagonal is 10 cm, find the perimeter of MNPQ.
, 46. For ?
47. In the figure, , E lies on side and so that bisect each other. If Copyright Cengage Learning. Powered by Cognero.
. For , what name is given to the line segment and is larger than , find , ,
.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
48. In , M is the midpoint of and N is the midpoint of expression (containing x) represents the length of ?
. If the length of is represented by 49. In rectangle ABCD, AB = 5 and BC = 4. As a square root, find the length of diagonal Copyright Cengage Learning. Powered by Cognero.
, what
.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
50. In kite ABCD, AB = AD = y 5, BC = y, and . Find the perimeter of ABCD.
51. For a trapezoid, the lengths of the two bases are a and b. What expression represents the length of the median of the
trapezoid?
52. In the figure, and bisects . Name the reason that justifies why
.
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
53. In , RS = 19, ST = 15, and WT = 10. Find the length of altitude 54. In trapezoid RSTV, .
. If m
55. In the figure, S-T-U-V and Copyright Cengage Learning. Powered by Cognero.
, m
, m
, and m
. Draw a conclusion regarding .
, find the value of the expression and .
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
56. The angle shown measures 60°. How would you construct an angle that measures 30°?
57. has a perimeter of 84 cm. If cm and ST = 25 cm, find the angle of greatest measure in .
58. For a quadrilateral to be “cyclic,” what requirement must be satisfied?
59. For kite MNPQ, and 60. In the figure, bisects the acute angle of is longest?
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. If diagonal of is drawn, what type of triangles are formed?
to form isosceles triangle ABD with base . Which side
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
61. In the figure, the measure of exterior angle BCD is twice the measure of .What type of triangle is ?
62. For a parallelogram to be a rhombus, what condition must it satisfy?
63. In a right triangle, the length of the hypotenuse is 13 inches and the length of one of the legs is 12 inches. Find the
length of the other leg.
64. Supply all statements and all reasons for the following proof.
Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
65. Use the given drawing and information to prove Theorem 3.1.1 (AAS). Provide all
statements and reasons.
Given: Prove: , , and 66. Use the drawing shown to explain the following theorem.
“The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases.”
Given: Trapezoid ABCD with median Prove: [Hint: X is the midpoint of auxiliary diagonal .]
67. Be sure you can construct any the constructions provided on the course website, and that you can justify the
constructions.​
68. ​Assuming the Theorem 4.1.1, be able to establish the corollaries 4.1.2, 4.1.3, 4.1.4, and 4.1.5
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Name: Class: Date: Practice Exam II - Chapters 3 & 4
69. Given the definition of a rectangle (see ​p. 187 or class notes) be able to establish the corollary 4.3.1, 4.3.2.
Similarly, given the definition of the square provided in the book, establish the corollary 4.3.3.
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