Honors Geometry 1st Semester Exam Review
1. Let be between and . Use the Segment Addition Postulate to solve for .
= = = 27
a. = 3 b. = 11 c. = –5 d. = 8
Fill in the correct word(s) to make the statement true.
2. Mathematical statements that are assumed to be
true are called ______.
3. a. Plot the following points in a coordinate plane: A
(–2, 2), B (3, 2), C (–2, –4), D (3, –4), b. Is congruent to ? Explain. c. Is there another pair of congruent segments? If so, name the segments and explain why they are congruent.
4. The diagonals of parallelogram ABCD have a
common midpoint.
A B
CD
10–10 x
10
–10
y
Which of the following is the midpoint of the diagonals of ABCD? a. b. c. d.
5. The midpoint of is . One endpoint is . Find the coordinates of the other endpoint.
M
J
10–10 x
10
–10
y
6. mJHI = ( )° and mGHI = ( )° and
mJHG = 65°. Find mJHI and mGHI.
a. mJHI = 19° and mGHI = 46° b. mJHI = 46° and mGHI = 19° c. mJHI = 13° and mGHI = 52° d. mJHI = 52° and mGHI = 13°
7. In the figure (not drawn to scale), bisects °, and
°. Solve for x and find
a. 2, 38° b. 2, 7° c. 7, 207° d. 7, 120°
8. You know that bisects BAC, and that mCAD is 45°.
a. Draw a sketch that shows that bisects BAC. b. Find the measure of BAC. Explain how you found your answer.
9. The nonshared sides of two adjacent angles form a
pair of opposite rays. The angles are _________. a. acute b. complementary c. a linear pair d. vertical angles
10. Name .
A
B
C
D
E
O
a. b. c. d.
11.
Name a pair of vertical angles in the figure above.
12. Goldbach's conjecture states: every even number
greater than 2 can be written as the sum of two prime numbers. Which sum for 30 supports this conjecture? a. 15+15 b. 12+18 c. 17+13 d. 2+28
13. State a counterexample to disprove the following conjecture: A hot air balloon is a device that floats in the air. a. Hot air balloons are red. b. Helium balloons also float. c. A car is also a device. d. Hot air is also warm.
14. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. What is the next number in the sequence
15. Explain what inductive reasoning is and give an
example.
16. Identify the hypothesis and conclusion of the statement. If today is Wednesday, then tomorrow is Thursday.
17. "If an obtuse angle is bisected, then two acute angles are obtained." Decide whether the statement and its converse are true. If false, explain.
18. Tell whether the converse of the following statement is True or False. If it is false, give a counterexample. "If a number is even, then it is a multiple of 4."
19. Write the inverse of the following statement. If a number is not even, then it is not divisible by two.
Decide whether the statement about the diagram is true. Explain your answer using definitions you have learned.
20.
21.
22. are a linear pair.
From the given true statements, make a valid conclusion:
23. If there is no more milk, Rita will go to the store.
There is no more milk.
24. If Joshua works on Sunday, he will not work on
Tuesday. If Joshua does not work on Tuesday, he will not work on Wednesday.
Open-ended:
25. Write a valid argument using the Law of Syllogism.
26. Make a truth table for the compound statement
. a.
b.
c.
d.
Choose the phrase that completes the following statement as stated by the Point, Line, and Plane Postulates:
27. One plane ____ passes through three noncollinear
points. a. always b. never c. sometimes d. Point, Line, and Plane Postulates do not address
this topic directly.
28. A line ____contains at least two points. a. always b. never c. sometimes d. Point, Line, and Plane Postulates do not address
this topic directly.
29. Two distinct points are ____ connected by two distinct lines. a. never b. always c. sometimes d. Point, Line, and Plane Postulates do not address
this topic directly.
30. If two distinct lines intersect, their intersection is ____ one point. a. always b. never c. sometimes d. Point, Line, and Plane Postulates do not address
this topic directly.
31. Which of the following is an example of the Transitive Property? a. b. c. d.
32. If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the __________. a. Substitution Property of Equality b. Multiplication Property of Equality c. Transitive Property of Equality d. Reflexive Property of Equality
Identify the property that makes the statement true.
33. If XY = MN, then MN = XY.
34. If mP = mR and mR = mT, then mP =
mT.
35. If MP = PQ and PQ = QR, then MP = QR.
36. If m1 + m2 = 25° and m1 = 9°, then
.
37. In the figure shown, . Which of the
following statements is false?
A
B
E
D
C
a. b. c. d.
38. are supplementary angles. are vertical angles. If what is a. b. c. d.
39. Provide reasons for each statement in the proof. Given: 3 4 Prove: 1 2
College Entrance Exam:
40. In the figure below, if l and k are parallel lines,
what is the value of x + y?
a. ° b. ° c. ° d. °
41. If is parallel to , what is the measure, in degrees, of ?
a. 28° b. 72°
c. 62° d. 38°
42. Lines a and b in the figure below are parallel.
What is the measure of in degrees?
Complete this two-column proof.
43. Given: Lines m and n are parallel.
Transversal t intersects lines m and n. Prove:
44. Refer to the figure. Which theorem guarantees l and m are parallel?
a. Alternate Interior Angles Converse b. Consecutive Interior Angles Converse c. Corresponding Angles Converse d. Alternate Exterior Angles Converse
45. Which lines, if any, must be parallel based on the given diagram and information. Give the justification for each conclusion.
a
b
c d
1 23 4
5 67 8
9 1011 12
13 1415 16
Which lines, if any, can be proved parallel given the following diagram?
46.
e
a b c d
32°70°
40°62°
47. Find the slope of the line passing through the points
A(6, –5) and B(–5, –7). a.
112
b. 112
c. 12 d. 2
11
48. Which best describes the relationship between Line 1 and Line 2? Line 1 passes through and
Line 2 passes through and a. perpendicular b. They are the same line. c. parallel d. neither perpendicular nor parallel
49. The graph below shows the taxi fares for rides of various distances in a large city.
How much does the fare increase with distance, expressed in terms of dollars per fraction of a mile? a. $0.35 per 0.2 mile b. c. $1.60 per 0.2 mile d.
50. Find the slope of a line perpendicular to the line containing the points (3, –7) and (4, –3).
51. Decide whether Line 1 and Line 2 are parallel,
perpendicular, or neither. Line 1 passes through (4, –6) and (6, –2) Line 2 passes through (7, –8) and (11, –6)
52. Writing: Explain the difference between a line having a slope of 0 and a line having an undefined slope. Give an example of an equation for each type of line.
53. Write an equation that is parallel to .
a.
b.
c.
d.
54. Find the slope-intercept form of the line passing through the point and parallel to the line
a.
238
b. c. d.
55. Which best describes the relationship between the lines with equations
? a. neither parallel nor perpendicular b. same line c. parallel d. perpendicular
56. What is the slope of a line perpendicular to the line ?
a. 2
9
b. 29
c. 9
2
d. 92
57. Write an equation that is perpendicular to
.
a. y = 2x – 3 b.
c.
d. y = –2x
58. Write the slope-intercept form of the equation of the line passing through the point (5, –4) and
perpendicular to the line
59. The graph shows the amount of water in a pool as it
is being drained. Write an equation of the line. What are the x- and y-intercepts? What do the intercepts mean in this situation?
60. Don opened a savings account with $300. Each
month, he will add $50 to the account. Let y represent the amount of money in the account after x months. Write an equation to model this situation. What do the slope and y-intercept mean in this situation?
61. Name a right triangle.
a. b. none of these c. d.
62. Refer to the figure below. .
a. 100° b. 17° c. 148°
d. 15°
63. Which pair of lengths can be two of the sides of an isosceles triangle which has a perimeter of 52 inches? a. 15 inches, 25 inches b. 15 inches, 22 inches c. 12 inches, 22 inches d. 16 inches, 21 inches
64. What is the value of z? (The figure may not be drawn to scale.)
a. b. c. d.
65. Complete the statement using one of the following words: always, sometimes, or never. "An isosceles triangle is an obtuse triangle."
66. Given:
Prove:
67. Refer to the figure below. Which of the following statements is true?
H
I
K
J
L
a. by HL c. by SAS b. by SSS d. There are no congruent triangles.
68. Given: Prove:
D
B
C
E
A
69. Given: and . What other piece
of information is needed to show by ASA Congruence Postulate? a. b. c. d. =
Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?
70.
71.
72.
73.
74. Given:
Prove:
75. In , AB = 3x – 2, BC = x + 4, and AC = 7.
Also . Which term does NOT describe ?
a. Equilateral b. Acute c. Isosceles d. Obtuse
76. Find the values of x and y.
a. x = 84°, y = 96° b. x = 84°, y = 64° c. x = 12°, y = 96° d. x = 12°, y = 84°
77. Given: Prove: is isosceles
78. Solve for x given = and = .
Assume B is the midpoint of and D is the midpoint of
A
B
C
D
E
a.
12
b. 4 c. 2 d.
14
79. For the triangle shown, VS = 5 and VQ = 6. Then PQ = ______.
a. 11 b. 12 c. 10 d. 5
80. Your town is holding local elections. The town sets up three polling stations around the area that form a triangle. They decide to meet at the circumcenter of their locations. The circumcenter is equidistant from the three of the triangle formed by the polling stations. a. vertices b. angles c. angle bisectors d. sides
81. If is the perpendicular bisector of , then KGF ______.
a. KHF b. FKG c. d. KFH
82. For the triangle, find the coordinates of the point of concurrency of the perpendicular bisectors of the sides.
5–5 x
5
–5
y
a. (1, 1) b.
(32 , 3
2)
c. (1
2 , 1)
d. (3
2 , 12)
83. Given: is the perpendicular bisector of . Which statement is true?
a. b. CM = BM c. is a right angle. d. C is the midpoint of
84. Given: bisects DAB . Find ED if and (not drawn to scale)
a. 51 b. 540 c. 39 d. 21
85. The angle bisectors of a triangle are concurrent at a point called the _____.
86. The incenter of a triangle is equidistant from the
three ____ of the triangle.
87. Use a straightedge and compass to construct the
incenter of the triangle shown and draw the inscribed circle.
Refer to the figure below.
Given: , ABE EBC
88. A median of is ____.
a. b. c.
d.
89. An altitude of is ____. a. b. c. d.
90. The medians of a triangle are concurrent. Their common point is the ____. a. centroid b. incenter c. orthocenter d. circumcenter
91. is an altitude of . Therefore, is ______. a. right b. equilateral c. isosceles d. acute
92. Refer to the figure.
The longest segment is ______. a. b. c. d.
93. Which side lengths allow you to construct a triangle? a. b. c. d.
94. Two sides of a triangle have lengths 7 and 13. The third side has a length that is ______. a. greater than 6 and less than 13 b. less than 20 and greater than 6
c. greater than 20 d. less than 6
95. In and , , , , , and Which
angle measure is reasonable for ?
a. 55° b. 65° c. 70° d. 60°
96. Which statement is false for the diagram?
a. b. c. d.
97. Refer to the figure below. Use the given information to complete the statement using <, >, or = .
Given: , m1 < m2 CD ______ DB
98. and are acute triangles, and
. Which triangle has the greater perimeter? Justify your answer.
99. If , which of the following is NOT true?
a.
b. PS = RQ
c.
d. PR = SQ
100. Mr. Jones has taken a survey of college students and found that 1 out of 5 students are liberal arts majors. If a college has 12,000 students, what is the best estimate of the number of students who are liberal arts majors? a. 60,000 b. 300 c. 2400 d. 240
101. Assume the exchange rate of Canadian dollars to American dollars is 1 to 0.77. If a stove costs $529.50 in Canadian dollars, then what would its price be in American dollars? a. $407.72 b. $452.50 c. $687.66 d. $506.50
102. The geometric mean of 5 and 15 is ______. a. b. 75 c. 3 d. 10
103. While visiting a daycare center, you estimate the ratio of toddlers to infants as If the center has an enrollment of 30 children, about how many of them are infants?
104. The measures of the angles of a triangle are in the
extended ratio of 7 : 9 : 10. Find the measures of the angles of the triangle.
105. A triangle with a perimeter of 63 feet has side
lengths in the extended ratio of 6 : 7 : 8. Find the side lengths of the triangle.
106. A blueprint shows the scale drawing of a house.
The length of one living room wall on the blueprint is 4 inches. The actual length of the wall is 10 feet. What is the scale of the blueprint?
107. Are the two polygons similar? (They are not drawn
to scale, but assume all angles are 90°.) If not, explain why.
5
68
2
25
3041
10
a. Yes b.
No;
c. not enough information to tell d.
No;
108. If two polygons are SIMILAR, then the corresponding angles must be _____. a. complementary b. supplementary c. congruent d. linear pairs
109. If two polygons are SIMILAR, then the corresponding sides must be _____. a. proportional b. congruent c. parallel d. similar
110. ABC and XYZ are similar with A = X, and B = Y. If AB, BC, and AC are 7 inches, 9 inches, and 10 inches, respectively, and XY is 9 inches, find XZ. a. 7 in. b. 7.8 in. c. 11.6 in. d. 12.9 in.
111. Given that ABC DEF, solve for x and y.
112. Which triangle below is not similar to any of the others?
113. Triangle ABC is similar to triangle DEF. The perimeter of is 108 centimeters. What is the length of
114. Two ladders are leaning against a wall at the same angle as shown.
How far up the wall does the shorter ladder reach? a. 16 ft b. 18 ft c. 22 ft d. 36 ft
115. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Late in the afternoon, a man who is 6 feet tall casts a 15-foot shadow. He is not far from a tower 68 feet tall. How long, in feet, is the shadow of the tower?
Tell whether each pair of triangles is similar. Explain your reasoning.
116.
Determine whether the triangles are similar. If the are, write a similarity statement.
117.
118.
119. One way to show that two triangles are similar is to
show that ______. a. two angles of one are congruent to two angles
of the other b. two sides of one are proportional to two sides
of the other
c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the
other
120. Shown below is an illustration of the ______.
a. AA Similarity Postulate b. SAS Congruence Theorem c. SSS Similarity Theorem
d. SAS Similarity Theorem
121. The postulate or theorem that can be used to prove that the two triangles are similar is _____.
a. SAS Similarity Theorem b. ASA Congruence Theorem c. SSS Similarity Theorem d. AA Similarity Postulate
122. What value of x will make the two triangles similar?
123. If ABC ~ PBQ, then which of the following proportions is NOT true?
a.
b.
c.
d.
The polygons in each pair are similar. Find the value of each variable.
124.
