Embed Size (px)
DESCRIPTION
Geometry EOC REview Packet
Citation preview
Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Geometry EOC Review Packet
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
Refer to Figure 1.
Figure 1
1. Name a line that contains point J.a. nb. p
c. DB→←
d. GF→←
2. Name a point NOT contained in lines m, n, or p.a. D
b. Kc. Hd. A
3. Name the plane containing lines m and p.a. Hb. GFCc. nd. JDB
4. What is another name for line n?
a. DC→←
b. ACc. line JB
d. GF→←
5. Does line p intersect line m or line n? Explain.a. No, the lines do not meet in this diagram.b. Yes, it intersects line n when both are
extended.c. Yes, it intersects line m when both are
extended.d. Yes, it intersects both m and n when all three
are extended.
6. Which of these is NOT a way to refer to line BD?a. line JD
b. JB→←
c. m
d. JDB→←
7. Name three points that are collinear.
a. J, D, Bb. J, B, Gc. A, G, Bd. B, J , H
Name: ________________________ ID: A
2
8. Are points B, A, D, and C coplanar? Explain.
a. No; three lie on the same face of the pyramid and the fourth does not.
b. No; one is on plane P.
c. Yes; they all lie on plane P.d. Yes; they all lie on the same face of the pyramid.
Find the measurement of the segment.
9. QT= 0.21 in., QV = 1.85 in.
TV = ?a. 1.54 in.b. 1.84 in.c. 1.64 in.d. 2.06 in.
10. Find the value of the variable and GH if H is between G and I.
GI = 7b + 2,HI = 3b − 5,HI = 22
a. b = 9, GH = 65 c. b = 2.5, GH = 19.5b. b = 2.86, GH = 25.57 d. b = 9, GH = 43
Name: ________________________ ID: A
3
Use the Distance Formula to find the distance between each pair of points.
11.
a. 34b. 5c. 6
d. 50
Find the coordinates of the midpoint of a segment having the given endpoints.
12. Q −9, 9ÊËÁÁ
ˆ¯̃̃ , R 5, − 1Ê
ËÁÁˆ¯̃̃
a. −2, 4ÊËÁÁ
ˆ¯̃̃
b. −14, 10ÊËÁÁ
ˆ¯̃̃
c. 0, 2ÊËÁÁ
ˆ¯̃̃
d. −7, 5ÊËÁÁ
ˆ¯̃̃
Classify the anges as right, acute, straight, or obtuse.
13. ∠4a. obtuseb. straightc. acuted. right
14. ∠BGDa. rightb. straightc. acuted. obtuse
In the figure, GK→
bisects ∠FGH.
15. If m∠FGK = 6v − 2 and m∠KGH = 2v + 6, find x.a. 10b. 20c. 2d. 12
16. If m∠FGK = 6w + 9 and m∠FGH = 126, find w.a. 63b. 4.5c. 9d. 19.5
Name: ________________________ ID: A
4
In the figure, KJ→
and KL→
are opposite rays.
∠1 ≅ ∠2 and KM→
bisects ∠NKL.
17. What bisects ∠JKN?
a. KP→
b. PK→
c. Pd. ∠2
18. Which is NOT true about KM→
?a. Point M lies in the interior of ∠LKN.b. ∠3 ≅ ∠MKLc. ∠MKJ is acute.d. It is an angle bisector.
19. If m∠JKM = 5x + 18 and m∠4 = x, what is m∠4?a. 153b. 12c. 27d. 33
20. If m∠JKP = 3r + 12 and m∠2 = 4r − 2, what is m∠JKN?a. 54b. 108c. 72d. 14
21. If m∠LKN = 6w − 10 and m∠JKP = 2w + 5, what is w?a. 18b. 9c. 10d. 41
Use the figure to find the angles.
22. Name two acute vertical angles.a. ∠GQI, ∠IQMb. ∠KQL, ∠KQMc. ∠HQL, ∠IQKd. ∠KQL, ∠IQH
23. Name a pair of obtuse adjacent angles.a. ∠HQG, ∠IQHb. ∠GQL, ∠LQJc. ∠KQG, ∠HQMd. ∠GQI, ∠IQM
24. Name a linear pair.a. ∠GQI, ∠IQMb. ∠GQL, ∠LQJc. ∠LQG, ∠KQMd. ∠KQG, ∠HQM
25. Name an angle supplementary to ∠MQI.a. ∠IQHb. ∠MQKc. ∠GQLd. ∠IQG
26. Name two obtuse vertical angles.a. ∠KQL, ∠IQHb. ∠GQI, ∠IQMc. ∠KQL, ∠KQMd. ∠HQL, ∠IQK
Name: ________________________ ID: A
5
27. The measures of two complementary angles are 12q − 9 and 8q + 14. Find the measures of the angles.a. 96, 84b. 8.75c. 4.25d. 42, 48
28. Two angles are supplementary. One angle measures 26o more than the other. Find the measure of the two angles.a. 32, 58b. 167, 193c. 77, 103d. 76, 104
29. The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from Springfield to Junction City. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch?
a. 125 mi c. 305 mib. 180 mi d. 145 mi
30. M is the midpoint of AN, A has coordinates (1, 8), and M has coordinates (–4, 2). Find the coordinates of N.a. (−8, −5)b. (–9, –4)c. (–3, 10)
d. (−11
2 , 5)
Make a conjecture about the next item in the sequence.
31. 1, 4, 16, 64, 256a. 4096b. 1022c. 1025d. 1024
32. 6, 2,− 4,− 8, 16a. 18b. 12c. −24d. −32
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
33. Given: points A, B, C, and DConjecture: A, B, C, and D are coplanar.a. False; the four points do not have to be in a
straight line.b. Truec. False; three points are always coplanar but four
are not.d. False; two points are always coplanar but four
are not.
34. Given: a concave polygonConjecture: It can be regular or irregular.a. False; a concave polygon has an odd number of
sides.b. False; all concave polygons are regular.c. False; to be concave the angles cannot be
congruent.d. True
35. Given: Point B is in the interior of ∠ADC.Conjecture: ∠ADB ≅ ∠BDCa. False; just because it is in the interior does not
mean it is on the bisecting line.b. False; m∠ADB may be obtuse.c. Trued. False; m∠ADB + m∠BDC = 90.
Name: ________________________ ID: A
6
36. Given: m2 + 6 = 10Conjecture: m= 2a. False; m= 3b. False; m= −2c. Trued. False; m= 4
37. Given: points R, S, and TConjecture: R, S, and T are coplanar.a. Trueb. False; one point may not be between the other
two.c. False; the points to not have to form right
angles.d. False; the points do not have to be in a straight
line.
38. Given: Two angles are supplementary.Conjecture: They are both acute angles.a. Trueb. False; either both are right or they are adjacent.c. False; either both are right or one is obtuse.d. False; they must be vertical angles.
39. Given: ∠F is supplementary to ∠G and ∠G is supplementary to ∠H.Conjecture: ∠F is supplementary to ∠H.a. False; they could be right angles.b. False; they could be congruent angles.c. Trued. False; they could be vertical angles.
40. Given:
Conjecture: ∠BCA≅ ∠BACa. False; the angles are not complementary.b. False; there is no indication of the measures of
the angles.c. Trued. False; the angles are not vertical.
Write the statement in if-then form.
41. Two angles measuring 90 are complementary.a. If the angles are complementary, then the
angles are complementary.b. If two angles measure 90, then the angles are
complementary.c. If the angles are supplementary, then two
angles measure 90.d. If two angles measure 90, then two angles
measure 90.
Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.
42. If you have a dog, then you are a pet owner.a. If you have a dog, then you are a pet owner. Trueb. If you are a pet owner, then you have a dog. False; you could own a hamster.c. If you are a pet owner, then you have a dog. Trued. A dog owner owns a pet. True
Name: ________________________ ID: A
7
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.
43. People who live in Texas live in the United States.a. People who do not live in Texas do not live in
the United States. False; they could live in Oklahoma.
b. People who do not live in Texas live in the United States. True
c. People who do not live in the United States do not live in Texas. True
d. People who live in the United States live in Texas. False; they could live in Oklahoma.
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.
44. If you are 16 years old, then you are a teenager.a. If you are not a teenager, then you are 16 years
old. Trueb. If you are a teenager, then you are 16 years old.
False; you could be 17 years old.c. If you are not a teenager, then you are not 16
years old. Trued. If you are not 16 years old, then you are not a
teenager. False; you could be 17 years old.
45. Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in California, then you are in the west coast. If you are in Los Angeles, then you are in California.
Conjecture: If you are in Los Angeles, then you are in the west coast.a. No, the conjecture is not valid.b. Yes, the conjecture is valid.
46. Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ and the part following then is the ____.a. hypothesis; conditional; conclusionb. hypothesis; conclusion; conditionalc. conditional; hypothesis; conclusiond. conditional; conclusion; hypothesis
47. What is the conclusion of the following conditional?A number is divisible by 2 if the number is even.a. The number is even.b. The number is divisible by 2.c. The number is even.d. If a number is even, then the number is
divisible by 2.
48. When a conditional and its converse are true, you can combine them as a true ____.a. counterexampleb. unconditionalc. biconditionald. hypothesis
49. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional.Two lines that intersect at right angles are perpendicular.a. Reversible; if two lines intersect at right
angles, then they are perpendicular.b. Reversible; two lines intersect at right angles if
and only if they are perpendicular.c. The statement is not reversible.d. Reversible; if two lines are perpendicular, then
they intersect at right angles.
50. One way to show that a statement is NOT a good definition is to find a ____.a. converseb. biconditionalc. conditionald. counterexample
51. Which statement is the Law of Detachment?a. If p → q is a true statement and q is true, then
p is true.b. If p → q is a true statement and p is true, then
q is true.c. If p → q and q → r are true, then p → r is
a true statement.d. If p → q is a true statement and q is true, then
q → p is true.
Name: ________________________ ID: A
8
52. Which statement is the Law of Syllogism?a. If p → q is a true statement and q is true, then
p is true.b. if p → q and q → r are true statements, then
p → r is a true statement.c. If p → q is a true statement and p is true, then
q is true.d. If p → q and q → r are true statements, then
r → p is a true statement.
53. Use the Law of Syllogism to draw a conclusion from the two given statements.If two lines intersect and form right angles, the lines are perpendicular.If two lines are perpendicular, they intersect and form 90° angles.a. If two lines do not intersect and form 90° angles, they do not form right angles.b. If two lines intersect and form right angles, they intersect and form 90° angles.c. The lines are perpendicular.d. The lines intersect and form 90° angles.
Fill in each missing reason.
54. Given: m∠PQR = x + 9, m∠SQR= x + 7, and m∠PQS= 100.Find x.
m∠PQR + m∠SQR = m∠PQS a. _____x + 9 + x + 7 = 100 b. Substitution Property
2x + 16 = 100 c. Simplify2x = 84 d. _____x = 42 e. Division Property of Equality
a. Protractor Postulate; Addition Property of Equalityb. Angle Addition Postulate; Subtraction Property of Equalityc. Angle Addition Postulate; Addition Property of Equalityd. Protractor Postulate; Subtraction Property of Equality
Name: ________________________ ID: A
9
55. Given: 8x − 5y = −4;x = 8
Prove: 685
= y
8x − 5y = −4;x = 8 a. ________
64− 5y = −4 b. ________
−5y = −68 c. ________
y = 685
d. ________
685
= y e. ________
a. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Addition Property of Equalitye. Symmetric Property of Equality
b. a. Givenb. Symmetric Property of Equalityc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality
c. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality
d. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Symmetric Property of Equality
56. Name the Property of Equality that justifies the statement:If m = n, then n = m.a. Addition Propertyb. Multiplication Propertyc. Symmetric Propertyd. Reflexive Property
57. Name the Property of Congruence that justifies the statement:
If ST≅ UV, thenUV ≅ ST.a. Transitive Propertyb. Reflexive Propertyc. Symmetric Propertyd. none of these
58. Name the Property of Congruence that justifies the statement:If ∠M ≅ ∠N and∠N ≅ ∠O, then∠M ≅ ∠O.a. Reflexive Property c. Symmetric Propertyb. Transitive Property d. none of these
Name: ________________________ ID: A
10
Use the given property to complete the statement.
59. Transitive Property of Congruence
If MN ≅ LK andLK ≅ OP, then ______.
a. MN ≅ LK
b. MN ≅ OP
c. LK ≅ LK
d. LK ≅ OP
Identify the sets of lines to which the given line is a transversal.
60. line i
a. lines m and p¸ n and ob. lines jc. lines m and n¸ n and o¸ m and o¸ m and p¸ n and
p¸ o and pd. lines m and n¸ n and o¸ m and o
61. line d
a. lines b and a¸ fb. lines b and a¸ a and f ¸ b and f c. lines a and f ¸ b and f d. lines d and a¸ d and b¸ d and c¸ d and f
62. In the figure, m∠NML = 120, PQ→←Ä TU
→←and
KL→←Ä NM
→←. Find the measure of angle QSN.
a. 100b. 60c. 120d. 40
63. In the figure, m∠RPZ= 95 and TU→←Ä RQ
→←Ä VW
→←.
Find the measure of angle YSV.
a. 65b. 75c. 95d. 85
Name: ________________________ ID: A
11
64. In the figure, AB Ä CD. Find x and y.
a. x = 47, y = 137b. x = 43, y = 141c. x = 27, y = 137d. x = 137, y = 47
65. In the figure, p Ä q. Find m∠1.
a. m∠1 = 42b. m∠1 = 48c. m∠1 = 64d. m∠1 = 68
Determine the slope of the line that contains the given points.
66. T 4, 5ÊËÁÁ
ˆ¯̃̃ , V 7, 6Ê
ËÁÁˆ¯̃̃
a. −1b. −3c. 3
d.13
Determine whether WX→←
and YZ→←
are parallel, perpendicular, or neither.
67. W −1, − 6ÊËÁÁ
ˆ¯̃̃ , X 3, 7Ê
ËÁÁˆ¯̃̃, Y 3, 5Ê
ËÁÁˆ¯̃̃, Z 4, 8Ê
ËÁÁˆ¯̃̃
a. perpendicularb. neitherc. parallel
Name: ________________________ ID: A
12
Write an equation in slope-intercept form of the line having the given slope and y-intercept.
68. m:− 27
, b:− 3
a. y = −3x − 27
b. y = 67
x
c. y = −27
x − 3
d. y = −37
x
Write an equation in point-slope form of the line having the given slope that contains the given point.
69. m= 5, 4, 3ÊËÁÁ
ˆ¯̃̃
a. y − 4 = 5(x − 3)b. y − 3 = 5(x − 4)c. y = 5x − 1d. y − 5 = 3(x − 4)
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.
70. ∠10≅ ∠4
a. a Ä b; congruent alternate exterior anglesb. a Ä b; congruent corresponding anglesc. c Ä d; congruent alternate exterior anglesd. c Ä d; congruent corresponding angles
Name: ________________________ ID: A
13
71. ∠LHO ≅ ∠NKP
a. c Ä d; congruent corresponding anglesb. a Ä b; congruent alternate exterior anglesc. c Ä d; congruent alternate exterior anglesd. a Ä b; congruent corresponding angles
72. Find the values of x and y.
a. x = 8, y = 50b. x = 32, y = 148c. x = 50, y = 8d. x = 148, y = 32
73. Find the value of the variable if m Ä l, m∠1 = 3x + 24 and m∠5 = 7x + 32. The diagram is not to scale.
a. –3b. –1c. 2d. –2
Name: ________________________ ID: A
14
74. Find the values of x and y. The diagram is not to scale.
a. x = 49, y = 65b. x = 65, y = 81c. x = 81, y = 65d. x = 81, y = 67
75. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary.a. correspondingb. same-side interiorc. acuted. alternate interior
76. Find m∠Q. The diagram is not to scale.
a. 60b. 70c. 120d. 102
Name: ________________________ ID: A
15
77. Which is a correct two-column proof?
Given: l Ä mProve: ∠p and ∠k are supplementary.
a.
Statements R e asons
1. l Ä m 1. Given
2. ∠p ≅ ∠k 2. Corresponding Angles
3. ∠d and∠c are supplementary. 3. Same-Side Exterior Angles
4. ∠c ≅ ∠k 4. Vertical Angles
5. ∠d and∠k are supplementary. 5. Substitution
b.
Statements R e asons
1. l Ä m 1. Given
2. ∠p ≅ ∠d 2. Vertical Angles
3. ∠b and∠k are supplementary. 3. Alternate Interior Angles
4. ∠c ≅ ∠k 4. Vertical Angles
5. ∠p and∠k are supplementary. 5. Same-Side Interior Angles
c.
Statements R e asons
1. l Ä m 1. Given
2. ∠p ≅ ∠d 2. Vertical Angles
3. ∠d and∠c are supplementary. 3. Same-Side Interior Angles
4. ∠c ≅ ∠k 4. Vertical Angles
5. ∠p and∠k are supplementary. 5. Substitution
d. none of these
Name: ________________________ ID: A
16
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.
78. If ∠8 measures 125, what is the sum of the measures of ∠1 and ∠4?a. 110b. 305c. 125d. 250
79. How are ∠6 and ∠3 related?a. correponding anglesb. same-side interior anglesc. alternate interior anglesd. none of these
80. m∠1 = 4x andm∠3 = 112. Find the value of x for p to be parallel to q. The diagram is not to scale.
a. 108b. 28c. 112d. 116
Find the measures of the sides of ∆ABC and classify the triangle by its sides.
81. A 7, 2ÊËÁÁ
ˆ¯̃̃ ,B −2, 4Ê
ËÁÁˆ¯̃̃ ,C 4, 7Ê
ËÁÁˆ¯̃̃
a. equilateral c. obtuseb. scalene d. isosceles
Name: ________________________ ID: A
17
Find each measure.
82. m∠1, m∠2, m∠3
a. m∠1 = 64, m∠2 = 48, m∠3 = 52b. m∠1 = 48, m∠2 = 71, m∠3 = 68c. m∠1 = 48, m∠2 = 61, m∠3 = 64d. m∠1 = 64, m∠2 = 71, m∠3 = 52
83. m∠1, m∠2, m∠3
a. m∠1 = 94, m∠2 = 88, m∠3 = 34 c. m∠1 = 79, m∠2 = 47, m∠3 = 27b. m∠1 = 94, m∠2 = 47, m∠3 = 27 d. m∠1 = 79, m∠2 = 32, m∠3 = 34
Name the congruent angles and sides for the pair of congruent triangles.
84. ∆LGF ≅ ∆XYT
a. ∠L ≅ ∠Y,∠G ≅ ∠T,∠F ≅ ∠X, LG ≅ YT,GF ≅ TX,LF ≅ YX
b. ∠L ≅ ∠T,∠G ≅ ∠X,∠F ≅ ∠Y, LG ≅ TX,GF ≅ XY,LF ≅ TY
c. ∠L ≅ ∠X,∠G ≅ ∠Y,∠F ≅ ∠T, LG ≅ XY,GF ≅ YT,LF ≅ XT
d. ∠L ≅ ∠T,∠G ≅ ∠Y,∠F ≅ ∠X, LG ≅ TY,GF ≅ YX,LF ≅ TX
Name: ________________________ ID: A
18
Determine whether ∆PQR≅ ∆STU given the coordinates of the vertices. Explain.
85. P −3, 2ÊËÁÁ
ˆ¯̃̃, Q −2, − 3Ê
ËÁÁˆ¯̃̃ , R −1, 4Ê
ËÁÁˆ¯̃̃ , S 2, 4Ê
ËÁÁˆ¯̃̃ , T 3, − 1Ê
ËÁÁˆ¯̃̃ , U 4, 6Ê
ËÁÁˆ¯̃̃
a. Yes; Both triangles have three acute angles.b. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle
STU.c. No; Two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.d. No; Each side of triangle PQR is not the same length as the corresponding side of
triangle STU.
Refer to the figure. ∆ARM, ∆MAX, and∆XFM are all isosceles triangles.
86. What is m∠RAM?a. 23b. 42c. 38d. 35
87. What is m∠MAX?a. 108b. 38c. 36d. 16
88. If m∠FXA = 96, what is m∠FXM?a. 18b. 16c. 24d. 12
89. Triangles ABC and AFD are congruent equilateral triangles. Find x and y.
a. x = 7
3 , y = 27
b. x = 7, y = 33
c. x = 7
3 , y = 28
d. x = 7, y = 27
90. Triangle RSU is an equilateral triangle. RT bisects
US. Find x and y.
a. x = 5
4 , y = 12
b. x = 5
4 , y = 6
c. x = 4, y = 12d. x = 4, y = 6
Name: ________________________ ID: A
19
Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
91. a. hexagon, convex, regularb. hexagon, convex, irregularc. pentagon, convex, regulard. hexagon, concave, regular
92.
a. triangle, convex, irregularb. quadrilateral, convex, irregularc. triangle, convex, regulard. triangle, concave, irregular
93.
a. quadrilateral, convex, irregularb. quadrilateral, convex, regularc. pentagon, convex, irregulard. quadrilateral, concave, irregular
94.
a. dodecagon, convex, irregularb. dodecagon, concave, irregularc. decagon, convex, irregulard. decagon, concave, irregular
Find the length of each side of the polygon for the given perimeter.
95. P = 72 units. Find the length of each side.
a. 9 units, 36 units, 4 units, 23 unitsb. 10 units, 34 units, 6 units, 22 unitsc. 9 units, 35 units, 5 units, 23 unitsd. 8 units, 33 units, 4 units, 21 units
Name: ________________________ ID: A
20
96. P = 100 ft. Find the length of each side.
a. 29 ft, 29 ft, 13 ft, 13 ft, 16 ftb. 50 ft, 50 ft, 20 ft, 20 ft, 30 ftc. 41 ft, 41 ft, 17 ft, 17 ft, 24 ftd. 33.5 ft, 33.5 ft, 14.5 ft, 14.5 ft, 19 ft
Find the circumference and the area of the figure. Solve in both terms of π and to the nearest tenth.
97.
a. 64π in.b. 16π in. c. 8π in. d. 4π in.
Find the area of the figure.
98.
a. 75.04 in2
b. 35.8 in2
c. 750.4 in2
d. 17.9 in2
Name: ________________________ ID: A
21
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
99. 6, 7, 15a. No; the sum of the lengths of two sides is not greater than the third.b. No; the first side is not long enough.c. Yes; the sum of the lengths of any twosides is greater than the third.d. Yes; the third side is the longest.
100. Find the values of x, y, and z. The diagram is not to scale.
a. x = 74, y = 57, z = 106b. x = 57, y = 74, z = 106c. x = 57, y = 106, z = 74d. x = 74, y = 106, z = 57
101. Given ∆ABC≅ ∆PQR, m∠B = 5v + 1, and m∠Q = 6v − 9, find m∠B and m∠Q.a. 51b. 52c. 72d. 69
102. Justify the last two steps of the proof.
Given: MN ≅ PO and MO ≅ PNProve: ∆MNO ≅ ∆PON
Proof:
1. MN ≅ PO 1. Given
2. MO ≅ PN 2. Given
3. NO ≅ ON 3. ?
4. ∆MNO ≅ ∆PON 4. ?
a. Reflexive Property of ≅; SSSb. Symmetric Property of ≅; SSSc. Reflexive Property of ≅; SASd. Symmetric Property of ≅; SAS
103. State whether ∆ABC and ∆AED are congruent. Justify your answer.
a. yes, by either SSS or SASb. yes, by SSS onlyc. yes, by SAS onlyd. No; there is not enough information to
conclude that the triangles are congruent.
Name: ________________________ ID: A
22
104. What is the missing reason in the two-column proof?
Given: MO→
bisects ∠PMN and OM→
bisects ∠PONProve: ∆PMO ≅ ∆MNO
Statements Reasons
1. MO→
bisects ∠PMN 1. Given2. ∠PMO ≅ ∠NMO 2. Definition of angle bisector3. MO ≅ MO 3. Reflexive property
4. OM→
bisects ∠PON 4. Given5. ∠PMO ≅ ∠NOM 5. Definition of angle bisector6. ∆PMO ≅ ∆NMO 6. ?
a. ASA Postulate c. AAS Theoremb. SAS Postulate d. SSS Postulate
105. Based on the given information, what can you conclude, and why?
Given: ∠H ≅ ∠L, HJ ≅ JL
a. ∆HIJ ≅ ∆LKJ by ASA c. ∆HIJ ≅ ∆JLK by ASAb. ∆HIJ ≅ ∆LKJ by SAS d. ∆HIJ ≅ ∆JLK by SAS
Name: ________________________ ID: A
23
106. If ∠A ≅ ∠D and ∠C ≅ ∠F, which additional statement does NOT allow you to conclude that ∆ABC ≅ ∆DEF?
a. BC ≅ EF c. ∠B ≅ ∠Eb. AB ≅ EF d. AC ≅ DF
107. Supply the missing reasons to complete the proof.
Given: ∠I ≅ ∠L and IJ ≅ LJ
Prove: HJ ≅ KJ
Statement Reasons
1. ∠I ≅ ∠L and
IJ ≅ LJ1. Given
2. ∠HJI ≅ ∠KJL 2. Vertical angles are congruent.
3. ∆HJI ≅ ∆KJL 3. ?
4.HJ ≅ KJ 4. ?
a. AAS; CPCTC c. ASA; Substitutionb. SAS; CPCTC d. ASA; CPCTC
Name: ________________________ ID: A
24
108. Find the value of x. The diagram is not to scale.
a. x = 60b. x = 21c. x = 15d. none of these
109. For which situation could you prove ∆1 ≅ ∆2 using the HL Theorem?
a. I and IIb. II onlyc. I onlyd. II and III
110. Find the measure of each interior angle for a regular heptagon. Round to the nearest tenth if necessary.a. 128.6b. 51.4c. 360d. 900
Name: ________________________ ID: A
25
111. Find the measure of each exterior angle for a regular octagon. Round to the nearest tenth if necessary.a. 45b. 360c. 135d. 1080
Complete the statement about parallelogram ABCD.
112. ∠ABC≅a. ∠ADC; Alternate interior angles are congruent.b. ∠BCD; Alternate interior angles are congruent.c. ∠ADC; Opposite angles of parallelograms are congruent.d. ∠BCD; Opposite angles of parallelograms are congruent.
Name: ________________________ ID: A
26
Refer to parallelogram ABCD to answer the following questions.
113. Do the diagonals bisect each other? Justify your answer.
a. No; AK ≅ CK and DK ≅ BKb. No; The diagonals are not congruent.c. Yes; The diagonals are not congruent.
d. Yes; AK ≅ CK and DK ≅ BK
Determine whether the quadrilateral is a parallelogram. Justify your answer.
114.
a. Yes; Consecutive angles are not congruent.b. Yes; Opposite angles are congruent.c. No; Opposite angles are congruent.d. No; Consecutive angles are not congruent.
Name: ________________________ ID: A
27
Determine whether a figure with the given vertices is a parallelogram.
115. A(−9, − 7), B(−6,− 8), C(−6, 9), D(−9, 10);
a. Yes; The diagonals have the same midpoint.b. No; The diagonals have the same midpoint.c. No; The opposite sides are congruent and have the same slope.d. Yes; The opposite sides are congruent and have the same slope.
Quadrilateral ABCD is a rectangle.
116. If AG = 2y + 29 and DG = −7y + 2, find BD.a. 23b. 11.5c. 46d. –3
117. If ∠ADB = −5h − 20 and ∠CDB = −3h + 70, find ∠CBD.a. 5b. 85c. 45d. –5
118. In rhombus QRST, if m∠QRT= 28, find m∠RSQ.
a. 124b. 28c. 56d. 62
Name: ________________________ ID: A
28
119. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
a. 58b. 2c. 29d. 26
120. At Whitewater Junior High School, there are 360 students and 39 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?a. 1:9.2b. 13:120c. 120:13d. 9.2:1
Solve each proportion.
121. 342
=g2
a. 34
b. 17
2
c. 1
34
d. 2
17
122. c + 1c − 1
= 222
a. − 5
6
b. 1
11
c. − 6
5
d. 11
Determine whether each pair of figures is similar. Justify your answer.
123.
a. ∆DEF is not similar to ∆CBA because the corresponding angles are not congruent.
b. ∆DEF ∼ ∆CBA because the ratio of the corresponding sides is proportional and the corresponding angles are congruent.
c. ∆DEF is not similar to ∆CBA because the ratio of the corresponding sides is not proportional.
d. ∆DEF ∼ ∆CBA because the corresponding angles are congruent.
Name: ________________________ ID: A
29
Determine whether each pair of triangles is similar. Justify your answer.
124.
a. yes; ∆EDF ∼ ∆BAC by SSS Similarityb. No; sides are not proportional.c. yes; ∆EDF ∼ ∆ABC by SSS Similarityd. yes; ∆EDF ∼ ∆BCA by SSS Similarity
125.
a. yes; ∆EDF ∼ ∆BCA by ASA Similarityb. No; the sides are not congruent.c. yes; ∆EDF ∼ ∆BCA by SAS Similarityd. yes; ∆EDF ∼ ∆BCA by SSS Similarity
Find x and the measures of the indicated parts.
126. AB
a. x = 7, AB = 4 c. x = 7, AB = 36b. x = 7, AB = 20 d. x = 7, AB = 16
Name: ________________________ ID: A
30
127. AB
a. x = 14
3 , AB = 28
3
b. x = 3
2 , AB = 6
c. x = 14
3 , AB = 28
d. x = 3
2 , AB = 3
Find the perimeter of the given triangle.
128. PQR, if PQR∼ PST, QR= 15, ST= 10, PS= 9, andPT = 8
a. 40.5b. 18c. 50.625d. 45
129. Find ST if QC and SD are altitudes and RQP∼ RST.
a. 19b. 17c. 5d. 7
130. Fran used a graphics program to reduce a digital image. The original dimensions of the image were 12 cm by 16 cm. She used a scale factor of 0.4. What are the dimensions of the reduction?
a. 9.6 cm by 4 cmb. 8.3 cm by 11.1 cmc. 2.5 cm by 10 cmd. 4.8 cm by 6.4 cm
131. The scale of a map is 0.5 inch : 40 miles. On the map, the distance between two cities is 5 inches. What is that actual distance between the two cities?
a. 380 milesb. 500 milesc. 400 milesd. 420 miles
132. Find the geometric mean between each pair of numbers.26 and 24a. 624
b. 5 2
c. 4 39d. 25
133. Find the geometric mean between each pair of numbers.
324 and 144a. 216
b. 30
c. 6 6d. 15
134. The length of a diagonal of a square is 29 2 millimeters. Find the perimeter of the square.a. 841 millimetersb. 1682 millimeters
c. 116 2 millimetersd. 116 millimeters
Name: ________________________ ID: A
31
135. Find x and y.
a. x = 14,y = 14 3
b. x = 28 3, y = 28
c. x = 28,y = 28 3
d. x = 14 3, y = 14
136. Find x and y.
a. x = 11 3, y = 11
b. x = 11,y = 11 3
c. x = 22,y = 22 3
d. x = 22 3, y = 22
137. Two swimmers are observed by a lifeguard in a 30-foot tower above the water. The angles of depression are 12.7° and 14.5°. How far apart are the swimmers?a. 17.1 ftb. 16.6 ftc. 133.1 ftd. 116.0 ft
138. After flying at an altitude of 500 meters, a hang glider starts to descend when the ground distance from the landing pad is 15 kilometers. What is the angle of depression for this part of the flight?a. 88.3°b. 1.7°c. 1.9°d. 88.1°
139. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
a. 162b. 3
c. 9 2d. 18
Name: ________________________ ID: A
32
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
140.
Not drawn to scale
a. x = 12, y = 36 3
b. x = 36, y = 12 3
c. x = 12 3, y = 36
d. x = 36 3, y = 12
141.
a. x = 18 3, y = 36
b. x = 36 3, y = 18
c. x = 18, y = 36 3
d. x = 36, y = 18 3
142. Find the value of x and y rounded to the nearest tenth.
a. x = 24.0, y = 46.4b. x = 48.1, y = 46.4c. x = 48.1, y = 139.3d. x = 24.0, y = 139.3
143. The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the perimeter.
a. 4 + 12 3
b. 6 + 2 3
c. 12 + 4 3
d. 2 + 6 3
144. A piece of art is in the shape of an equilateral triangle with sides of 12 in. Find the area of the piece of art. Round your answer to the nearest tenth.a. 62.4 in.2
b. 50.9 in.2
c. none of thesed. 124.7 in.2
145. Write the tangent ratios for ∠Y and ∠Z.
a. tanY =852
; tanZ =859
b. tanY = 92
; tanZ = 29
c. tanY = 2
85; tanZ = 9
85
d. tanY = 29
; tanZ = 92
Name: ________________________ ID: A
33
Find the value of x to the nearest degree.
146.
a. 55b. 42c. 35d. 59
147. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building.
a. 2400 ftb. 308 ftc. 33 ftd. 72 ft
Find the value of x. Round to the nearest tenth.
148.
a. 6.9b. 12.1c. 7d. 11.7
149.
a. 6.5b. 55.6c. 6.6d. 56.1
Name: ________________________ ID: A
34
Find the value of x. Round to the nearest degree.
150.
a. 46b. 40.5c. 44d. 35
151.
a. 40b. 34c. 32d. 56
152. Viola drives 200 meters up a hill that makes an angle of 9° with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?a. 1262.8 mb. 199.3 mc. 31.3 md. 197.5 m
153. Find x, y, and z.
a. x = 3, y = 4, z = 153
b. x = 5 2, y = 5 3, z = 5 5
c. x = 5, y = 5 2, z = 5 7
d. x = 2.5, y = 5 5
2 , z = 5 5
154. To estimate the height of a radio tower, Jody steps 25 feet away from the center of the tower’s base, until his line of sight to the top of the tower and his line of sight to the center of its base form a right angle. His eyes are 6 feet above the ground. How tall is the radio tower to the nearest foot?
a. 98 feetb. 110 feetc. 104 feet d. 31 feet
Name: ________________________ ID: A
35
155. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.
a. 30 m; 86.6 m2
b. 60 m; 86.6 m2
c. 60 m; 173.2 m2
d. 30 m; 173.2 m2
Find the area of the figure. Round to the nearest tenth if necessary.
156.
a. 764.7 units2
b. 300.3 units2
c. 366.7 units2
d. 249.7 units2
157.
a. 1920 units2
b. 960 units2
c. 480 units2
d. 240 units2
158.
a. 67.7 units2
b. 69.1 units2
c. 66.2 units2
d. 132.48 units2
159.
a. 41.5 units2
b. 74 units2
c. 50.5 units2
d. 56.5 units2
Name: ________________________ ID: A
36
160.
a. 41.1 units2
b. 47.3 units2
c. 57.1 units2
d. 66.2 units2
161. Find the area of a regular octagon with apothem length of 13.3 kilometers. Round to the nearest tenth if necessary.a. 73.15 units2
b. 585.2 units2
c. 1170.4 units2
d. 146.3 units2
162. An isosceles triangle has area of 150 ft2. If the base is 18 ft, what is the length of the legs? Round your answer to the nearest tenth.a. 17.3 ftb. 18.9 ftc. 601.8 ftd. 24.5 ft
Find the area of the trapezoid. Leave your answer in simplest radical form.
163.
a. 46.5 cm2
b. 27 cm2
c. 78 cm2
d. 15.5 cm2
164. Find the area of a regular hexagon with an apothem 8.7 inches long and a side 10 inches long. Round your answer to the nearest tenth.a. 519.6 in.2
b. 259.8 in.2
c. 173.2 in.2
d. 43.3 in.2
165. Find the area of an equilateral triangle with side 3.
a.94
3
b.34
3
c. 4.5d. 2.25
166. Find the area of an equilateral triangle with radius
4 3 m. Leave your answer in simplest radical form.
a. 36 3 m2
b. 6 3 m2
c. 9 3 m2
d. 24 3 m2
167. A regular hexagon has a perimeter of 140 m. Find its area. Leave your answer in simplest radical form.
a. 4900 3 m2
b.2450
33 m2
c.356
3 m2
d. 2450 3 m2
Name: ________________________ ID: A
37
168. Three towns, Maybury, Junesville, and Cyanna, will create one sports center. Where should the center be placed so that it is the same distance from all three towns?a. Treat the towns as vertices of a triangle. The
center must be placed at the triangle’s circumcenter.
b. Treat the towns as vertices of a triangle. The center must be placed at the triangle’s incenter.
c. Treat the towns as sides of a triangle. The center must be placed at the triangle’s circumcenter
d. Treat the towns as sides of a triangle. The center must be placed at the triangle’s incenter.
169. In ∆ABC, BY= 3.3 andCO = 3. Find BO.
a. BO = 2.2b. BO = 1.1c. BO = 3.3d. BO = 3
ID: A
1
Geometry EOC Review PacketAnswer Section
MULTIPLE CHOICE
1. C 2. C 3. B 4. A 5. D 6. D 7. A 8. A 9. C 10. D 11. A 12. A 13. C 14. C 15. A 16. C 17. A 18. C 19. C 20. B 21. A 22. D 23. B 24. A 25. D 26. D 27. D 28. C 29. A 30. B 31. D 32. B 33. C 34. C 35. A 36. B 37. A 38. C 39. B
ID: A
2
40. B 41. B 42. B 43. A 44. C 45. B 46. C 47. B 48. C 49. B 50. D 51. B 52. B 53. B 54. B 55. D 56. C 57. C 58. B 59. B 60. C 61. B 62. B 63. D 64. A 65. D 66. D 67. B 68. C 69. B 70. C 71. B 72. C 73. D 74. C 75. B 76. A 77. C 78. D 79. C 80. B 81. B 82. B 83. D 84. C
ID: A
3
85. B 86. C 87. C 88. C 89. D 90. D 91. A 92. A 93. A 94. D 95. C 96. A 97. B 98. A 99. A 100. A 101. A 102. A 103. A 104. A 105. A 106. C 107. D 108. B 109. D 110. A 111. A 112. C 113. D 114. B 115. A 116. C 117. A 118. D 119. D 120. D 121. A 122. C 123. A 124. D 125. C 126. B 127. D 128. A 129. D
ID: A
4
130. D 131. C 132. C 133. C 134. D 135. A 136. B 137. A 138. C 139. C 140. B 141. A 142. A 143. B 144. A 145. D 146. A 147. B 148. D 149. B 150. C 151. B 152. D 153. D 154. B 155. C 156. C 157. C 158. C 159. A 160. A 161. B 162. B 163. A 164. B 165. A 166. A 167. B 168. A 169. A
