learning target 1.1 identify points, lines, and planes

Geometry A Name _____________________________

Final Exam Review Date ___________________ Hour _____

Learning Target 1.1 – Identify Points, Lines, and Planes

Use the diagram to answer the following questions with either True or False.

1. Points A, B and C are collinear. ______

2. Points A and B are collinear. ______

3. Points C, B, and D are collinear. ______

4. Points A, B, and E are coplanar. ______

5. Points A, B, E and C are coplanar on plane F. ______

6. Another name for plane F is ABE. ______

7. The intersection of two planes is a line. ______

8. The intersection of two lines is a point. ______

Learning Target 1.2 – Use Segments and Congruence

9. M is the midpoint of the segment. Find XY.

10. Let J be between H and K on HK . Use the Segment Addition Postulate to solve for x

If HJ = 2x – 3, JK = 4x – 10, and KH = 17. Then find HJ and JK. Hint: Draw a picture and label it.

x = ______ HJ = ______ JK = ______

11. The notation for the length of the segment between S and T is _____.

A. ST B. ST C. ST D. ST

12. If AM = 23 and AB = 53, find the length of MB .

● ● ●

A M B

Learning Target 1.3 – Use Midpoint and Distance Formulas

13. Find the coordinates of the midpoint of the segment with the given endpoints.

R(3, 4) and S( –9, – 4)

14. What is the distance between points C(–4, 5) and D(2, –1).

4x – 10

8

2x – 2

2

B ●

A

● C

●

●

D

U ●

F●

●

N

M

●

2

3

1

4

Learning Target 1.4 – Measure and Classify Angles

15. If X Y and 65m Y , then what is m X ?

16. The measure of R is 100°. Classify R as

A. acute B. obtuse C. right D. straight

17. The measure of T is 89°. Classify T as

A. acute B. obtuse C. right D. straight

18. If 26m ABC and 73m ABD , the what is the measure of CBD ?

19. If FUM is acute and FUN is right, then MUN is what kind of angle?

A. acute B. obtuse

C. right D. straight

Learning Target 1.5 – Describe Angle Pair Relationships

For questions 20 – 23 refer to the figure at the right.

20. What type of angle pair is 1 and 2 ?



23. If 1m = 5x + 110 and 2m = 10x + 40, then solve for x.

24. If A and B are complementary and 20m A , then ______m B .

25. If C and D are supplementary and 50m C , then ______m D .

26. If E and F form a linear pair and 60m E , then ______m F .

3

Learning Target 3.1 – Identify Pairs of Lines and Angles

Use the cube to the right to answer the following questions.

(parallel, perpendicular, or skew).

27.

WZ and

WQ are what type of lines?

28.

WZ and

RS are what type of lines?

29.

WZ and

QR are what type of lines?

Use the diagram to complete the next six statements with:

A. Corresponding Angles B. Alternate Interior Angles

C. Alternate Exterior Angles D. Consecutive Interior Angles

30. l and 7 31. 4 and 6

32. 3 and 6 33. 2 and 6

34. 1 and 5 35. 2 and 8

Learning Target 3.2 – Use Parallel Lines and Transversals

Use the figure to the right to find the measure of each angle.

36. ml = 37. m5 =

1 2 3 4

38. m2 = 39. m6 = 5 6 115° 7

40. m3 = 41. m7 =

Find the value of x.

42. 43.

Use the diagram below and the given information to determine if m // n, p // q, or neither.

44. 2 11 45. 1 8

46. 10 14 47. 2 l0

4

Learning Target 3.3 – Prove Lines are Parallel

Use the given angle measures to decide whether lines p and q are parallel for the next two

questions.

48. m3 = 86°, 49. m1 = 63°,

m6 = 94° m6 = 117°

Use the diagram above to answer the following questions as True or False. (assume a // b)

50. 4 and 6 are supplementary angles?

51. 2 and 7 are congruent angles?

52. 3 and 6 are not congruent angles?

53. 3 and 5 are congruent angles?

Learning Target 3.4 – Find and Use Slope of Lines

54. Find the slope of the line that passes through the points (2, 5) and (7, 3). Then state the

slope of the line parallel and perpendicular to the calculated slope.

55. Find the slope of the line that passes through the points (–3, 1) and (0, 3). Then state the

slope of the line parallel and perpendicular to the calculated slope.

Learning Target 3.5 – Write and Graph Equations of Lines

56. Are lines 2 5y x and 1

32

y x parallel, perpendicular, or neither?

57. What would the slope of a line be that was perpendicular to 1

25

y x ?

58. What would the slope of a line be that was parallel to 4 2 8x y ?

59. Write an equation in slope-intercept form that passes through the point (0, 7)

and has a slope of 1

2.

60. Write an equation in slope-intercept form that passes through the point (1, 5)

and has a slope of 2.

a

b

5

61. Write an equation in slope-intercept form that is parallel to 3

24

y x and passes through

point (0, 0).

62. Write an equation in slope-intercept form that is perpendicular to 1

42

y x and passes

through point (2, 1).

Learning Target 3.6 – Prove Theorems about Perpendicular Lines

63. True or False. If two lines are perpendicular to the same transversal, then they are

parallel.

64. True or False. If two lines are perpendicular, then they intersect to form two right angles.


65. 66.

Learning Target 4.1 – Apply Triangle Sum Properties

For problems 67 – 70, classify the triangle by its side lengths or angles.

67. No congruent sides 68. Angles measures: 25°, 130°, 25°

69. Angles measures: 60°, 60°, 60° 70. Side lengths: 10cm, 10cm, 10cm


71. 72. 73.

4x°

5x°

6

74. Find m DBC . 75. Find the value of x.

Learning Target 4.2 – Apply Congruence and Triangles

Given, ABC DEF. Complete the statement.

76. ____ 77. A ___ 78. E ____

79. mC = ____ 80. AC = ____ 81. CBA ____

Write the correct congruence statement for these triangles.

82. ______ _______

Learning Targets 4.3 – 4.5 – Prove Triangle Congruence by SSS, SAS, HL, ASA, AAS &

Use Congruent Triangles (CPCTC)

Using the diagrams, choose the appropriate postulate or theorem that proves triangle

congruence:

A. SAS B. SSS C. ASA D. AAS E. HL

83. 84. 85.

Using the diagrams, choose the appropriate postulate or theorem that proves triangle

congruence:

A. SAS B. SSS C. ASA D. AAS E. HL

86. 87. 88.

89. 90. 91.

EF

D

A B C

50°

7

X Y

W Z

92. Proof Given: UVSVUTST ,

Prove: TSV TUV

Statements Reasons

1. UVSVUTST ,

2. TVTV

3. TSV TUV

4. TSV TUV

1.

2.

3.

4.

93. Proof Given: XYWZXYWZ ,//

Prove: XWZ ZYX

Statements Reasons

1. XYWZXYWZ ,//

2. XZXZ

3. YXZWZX

4. XWZ ZYX

1.

2.

3.

4.

Learning Target 4.7 – Use Isosceles and Equilateral Triangles

94. Find m B . 95. Find the value of x.

B

27°

A C

96. In SAT , if ATSA and m S 44°, then find the m T .

8

Learning Target 5.1 – Midsegment Theorem and Coordinate Proof

Use WXY, where R, S, and T are midpoints of the sides.

97. If RS = 20, then WY = ___________

98. RT ________ and ________

99. If the perimeter of RST is 60, then

the perimeter of WXY is ___________.


100. 101.

2x – 2

2x 8x – 16

2x + 8

Learning Target 5.2/5.3/5.4 – Use Perpendicular Bisectors, Angle Bisectors, Medians and

Altitudes of Triangles

Use the figure for the next three questions. In ABC , BD is an angle bisector, 39m DBC ,

and BF FC .

102. Find mBAC.

103. Identify a median of ABC.

104. Identify an altitude of ABC.

105. You can balance a triangle-shaped object by finding the centroid of the triangle. The length

of one median is 24 centimeters. How far from the vertex of the angle that the median was

drawn is the centroid?

9

Y

T

U

Z P M X

R

A

106. In the diagram, L is the centroid of 107. BD is a median of ABC. Find x.

MNO and LQ = 4. Find OQ.

8x – 12 3x + 33

For Questions 108 – 112, refer to the figure at the right.

* Consider that MZXM

108. Name the altitude of XYZ _________ .

109. Name the median of XYZ _________ .

110. Name the angle bisector of XYZ _________ .

111. Name the perpendicular bisector of XYZ _________ .

112. If 15ZYPm , then __________XZYm .

Learning Target 5.5 – Use Inequalities in a Triangle

Use the diagram below to list the following:

113. Sides in order from least to greatest. 114. Angles in order from least to greatest.

115. Sides in order from least to greatest. 116. Angles in order from least to greatest.

10

Determine whether it is possible to draw a triangle with sides of the given length.

117. 1, 3, 6 118. 12, 17, 33 119. 5, 2, 6 120. 3, 4, 5

Learning Target 5.6 – Inequalities in Two Triangles and Indirect Proofs

Complete the statements with <, >, or =.

121. m1 _____ m2 122. AT _____ BT

123. TP _____ AG 124. KD _____ CP

Learning Target 6.1 – Ratios & Proportions

Simplify the ratio or solve the proportion.

125. 10 .

3 .

in

ft 126.

10 6

5y y

127.

3 4 2

6 5

x x

128. A survey found that 2 out of 7 students take a gym class per semester. If a high school has

4200 students, what is the estimate of the number of students that are taking a gym class?

129. It took you 20 minutes to burn 123 calories while exercising. At that rate, how many

calories can you burn in 35 minutes?

130. The perimeter of a rectangle is 144 inches. The extended ratio of the length to the width

is 5:3. Find the length and the width of the rectangle. What is the area of the rectangle?

11

6 8

62°

A

B

C D

E

12

Learning Target 6.2 – Use Proportions to Solve Geometry Problems

131. If the exchange rate of the Euro to the American dollar is 0.81 to 1 and an Italian leather

jacket costs 714 Euros, then what would its price be in American dollars?

132. On a map, two neighboring towns are 2.4 inches apart. The map has a scale of 1 in : 15 miles.

What is the actual distance between the two towns?

133. Given , find WV.

Learning Target 6.3 – Use Similar Polygons

134. Give the definition of two SIMILAR polygons.

135. ΔABC and ΔDEF are similar with DA , EB , and C F . If AB, BC, and

AC are 2 inches, 5 inches, and 9 inches, respectively, and DE is 6 inches, find DF.

Learning Target 6.4 – Prove Triangles Similar by AA ~

136. Find the value of x if m A m R .

A

R

x = ___________

x 4 cm

scale factor = __________

C B T S

15cm 6cm

137. Find m ABC and AE.

YZ XY

WV XW

12

6

24.3 53°

T

A

H P

M

53° 51.4

21.7 x

11

14

21

6.1 ft

|------- 45 feet ---------------|

Mirror 12 feet

138. Jeremy wants to measure the height of the streetlight outside his house. He places a mirror

on the ground 45 feet from the streetlight, then walks backward until he is able to see the top of

the streetlight in the mirror. His eyes are 6.1 feet above the ground, and he is 12 feet from the

mirror. What is the height of the streetlight to the nearest tenth of a foot?

Learning Target 6.5 – Prove Triangles Similar by SSS~ and SAS~

139. ΔLMN ~ ΔPQR Find QR. 140. STUV ~ XYZW Find SV.

Learning Target 6.6 – Use Proportionality Theorems

Use the given information to determine if //AE BD

141. 142.

143. Find the value of x. 144. Given that //ST UV . Find x.

145. Find the value of z. 146. Find AB.

learning target 1.1 identify points, lines, and planes

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