Geometry A Name _____________________________ Midterm 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, and C are coplanar. ______ 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

4x – 10 8

2x – 2

2

B ●

A ● C

●

● D

U ●

F●

● N

M ●

2

3

1

4

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). Learning Target 1.4 – Measure and Classify Angles 15. If X Y∠ ≅ ∠ and 65m Y∠ = o, 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∠ = oand 73m ABD∠ = o, 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∠ ? 21. What type of angle pair is 1∠ and 3∠ ?

22. What type of angle pair is 2∠ and 4∠ ?

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

3

24. If A∠ and B∠ are complementary and 20m A∠ = o, then ______m B∠ = . 25. If C∠ and D∠ are supplementary and 50m C∠ = o, then ______m D∠ = . 26. If E∠ and F∠ form a linear pair and 60m E∠ = o, then ______m F∠ = . 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. m∠l = 37. m∠5 =

1 2 3 4 38. m∠2 = 39. m∠6 = 5 6 115° 7 40. m∠3 = 41. m∠7 = Find the value of x. 42. 43.

4

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 Learning Target 3.3 – Prove Lines are Parallel Use the given angle measures to decide whether lines a and b are parallel for the next two questions. 48. m∠3 = 86°, 49. m∠1 = 63°, m∠6 = 94° m∠6 = 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= − + ?

a

b

5

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 12

.

60. Write an equation in slope-intercept form that passes through the point (1, 5) and has a slope of 2.

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. Find the value of x. 65. 66. Learning Target 4.1 – Apply Triangle Sum Properties For problems 1 – 4, 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

6

Find the value of x. 71. 72. 73. 4x°

5x°

74. Find m DBC∠ . 75. Find the value of x. Learning Target 4.2 – Apply Congruence and Triangles Given, ΔABC ≅ ΔDEF. Complete the statement.

76. ≅ ____ 77. ∠A ≅ ___ 78. ∠E ≅ ____ 79. m∠C = ____ 80. AC = ____ 81. ΔCBA ≅ ____ Write the correct congruence statement for these triangles. 82. Δ ______ ≅ Δ _______ 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.

EF

D

A B C 50°

7

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. 92. Proof Given: UVSVUTST ≅≅ , Prove: TSV TUV∠ ≅ ∠ Statements Reasons

1. UVSVUTST ≅≅ , 2. TVTV ≅ 3. TSV TUVΔ ≅ Δ 4. TSV TUV∠ ≅ ∠

1. 2. 3. 4.

93. Proof Given: XYWZXYWZ ≅, Prove: XWZ ZYXΔ ≅ Δ Statements Reasons

1. XYWZXYWZ ≅, 2. XZXZ ≅ 3. 4. XWZ ZYXΔ ≅ Δ

1. 2. 3. 4.

8

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 SATΔ , if ATSA≅ and m S∠ = 44°, then find the m T∠ . Learning Target 5.1 – Midsegment Theorem and Coordinate Proof Use ΔWXY, where R, S, and T are midpoints of the sides. 97. If RS = 20, then WY = ___________ 98. RT ≅ ________ and ________ 99. If the perimeter of ΔRST is 60, then the perimeter of ΔWXY is ___________. Learning Target 5.2 – Use Perpendicular Bisectors Find the value of x. 100. 101. 2x – 2 2x 8x – 16 2x + 8

9

Learning Target 5.3/5.4 – Use Angle Bisectors of Triangles & Use Medians and Altitudes Use the figure for the next three questions. In ABCΔ , BD is an angle bisector 39m DBC∠ = o , and BF FC= . 102. Find m∠BAC.

103. Identify a median of ΔABC. 104. Identify an altitude of ΔABC. 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?

106. In the diagram, L is the centroid of 107. BD is a median of ΔABC. Find x. ΔMNO and LQ = 4. Find OQ. 8x – 12 3x + 33 Learning Target 5.5 – Use Inequalities in a Triangle Use the diagram below to list the following: 108. Sides in order from least to greatest. 109. Angles in order from least to greatest. 110. Sides in order from least to greatest. 111. Angles in order from least to greatest.

10

Determine whether it is possible to draw a triangle with sides of the given length. 112. 1, 3, 6 113. 12, 17, 33 114. 5, 2, 6 115. 3, 4, 5 Learning Target 5.6 – Inequalities in Two Triangles and Indirect Proofs Complete the statements with <, >, or =.

116. m∠1 _____ m∠2 117. AT _____ BT

118. TP _____ AG 119. KD _____ CP Learning Target 6.1 – Ratios & Proportions Simplify the ratio or solve the proportion.

120. 10 .3 .inft

121. 10 65y y=

− 122. 3 4 2

6 5x x− −

=

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

calories can you burn in 35 minutes? Learning Target 6.2 – Use Proportions to Solve Geometry Problems 125. 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?

11

6 8 62°

A

B

C D

E

12

6.1 ft

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

Mirror 12 feet

126. 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?

127. Given , find WV. Learning Target 6.3 – Use Similar Polygons 128. Give the definition of two SIMILAR polygons. 129. 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 ~ 130. Find the value of x if m A m R∠ = ∠ . A R x = ___________ x 4 cm scale factor = __________ C B T S 15cm 6cm 131. Find m ABC∠ and AE. 132. 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?

YZ XY

WV XW =

12

6

24.3 53°

T

A

H P

M

53° 51.4

21.7 x

11

14

20 z−21 z

Learning Target 6.5 – Prove Triangles Similar by SSS~ and SAS~ 133. ΔLMN ~ ΔPQR Find QR. 134. STUV ~ XYZW Find SV. Learning Target 6.6 – Use Proportionality Theorems Use the given information to determine if //AE BD 135. 136. 137. Find the value of x. 138. Given that //ST UV . Find x. 139. Find the value of z. 140. Find AB.

13

Chapter 1 ANSWER KEY 1. F 2. T 3. T 4. T 5. F 6. T 7. T 8. T

9. x = 4 ; XY = 12 10. x = 5; HJ = 7; JK = 10 11. C

12. MB = 30 13. (– 3, 0) 14. CD = 72 6 2 8.5= ≈

15. m X∠ = 65° 16. B 17. A

18. m CBD∠ = 47° 19. A 20. Supplementary & Linear Pair

21. Vertical Angles 22. Vertical Angles 23. x = 2 24. m 70° 25. m 130° 26. m 120°

Chapter 3 ANSWER KEY 27. Perpendicular 28. Skew 29. Parallel 30. C – AEA

31. B – AIA 32. D – CIA 33. A – Corr. 34. A – Corr. 35. C – AEA 36. 65° 37. 115° 38. 115°

39. 65° 40. 65° 41. 65° 42. x = 48 43. x = 80 44. m//n 45. p//q 46. p//q

47. m//n 48. No – AIA should be congruent. 49. Yes – Using a Jog: Corr. to a Linear Pair 50. True (CIA)

51. True (AEA) 52. False (AIA ≅ ) 53. False (CIA – supp.)

54. 25

− || slope = 25

− ⊥ slope = 52

55. 23

|| slope = 23

⊥ slope = 32

−

56. Perpendicular 57. m = 5 58. m = –2

59. 1 72

y x= + 60. y = 2x + 3 61. y = x

62. y = –2x + 5 63. True 64. False (should be 4 right angles)

65. x = 50 66. x = 40 Chapter 4 ANSWER KEY 67. scalene 68. obtuse, isosceles 69. equiangular, equilateral

70. equilateral, equiangular 71. x = 10 72. x = 25 73. x = 26 74. 140m DBC∠ = ° 75. x = 120°

76. BC 77. D∠ 78. B∠

79. m F∠ 80. DF 81. FEDΔ

14

Chapter 4 ANSWER KEY (con’t.) 82. LNP PSLΔ ≅ Δ 83. B – SSS 84. C – ASA

85. E – HL 86. C – ASA 87. D – AAS 88. A – SAS 89. D – AAS 90. E – HL 91. B – SSS

92. 1. Given 2. Reflexive Property of ≅ 3. SSS 4. CPCTC 93. 1. Given 2. Reflexive Property of ≅ 3. AIA are ≅ 4. SAS

94. 126m B∠ = ° 95. x = 3 96. m T∠ = 44° Chapter 5 ANSWER KEY

97. WY = 40 98. XS ; SY 99. 120

100. x = 4 101. x = 3 102. 51m BAC∠ = °

103. AF because BF FC= 104. BD 105. 16 cm.

106. OQ = 12 107. x = 9 108. , ,QR PR PQ or , ,QR PQ PR

109. , ,E D F∠ ∠ ∠ 110. , ,JK JL KL 111. , ,B C A∠ ∠ ∠

112. No 113. No 114. Yes 115. Yes 116. > 117. > 118. = 119. <

Chapter 6 ANSWER KEY

120. 518

121. 7.5− 122. 319

−

123. 1,200 students 124. 215.25 calories 125. $881.48 American

126. 36 miles 127. WV = 23

128. All angles are congruent; all sides are proportional

129. 27 in. 130. x = 10; 52

131. m 62° ; AE = 16

132. 22.9 feet 133. QR = 20 134. SV = 12 135. Yes 136. No 137. x = 45.9

138. x = 2 139. z = 11.2 140. AB = 15