1 Geometry Goncepts I: Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. In the diagram, the dashed figure is the image of the solid figure. 1. Name the image of ∠E. a. ∠T b. ∠Q c. ∠F d. ∠R 2. Name the image of DE . a. TQ b. RF c. QR d. FT 3. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of the image reflected in the x-axis. a. P " (3, 8), Q " (6, − 4), R " ( −1, 1) c. P " ( −3, − 8), Q " ( −6, 4), R " (1, − 1) b. P " ( −3, 8), Q " ( −6, − 4), R " (1, 1) d. P " (3, − 8), Q " (6, 4), R " ( −1, − 1) 4. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of the image reflected in the y-axis. a. P " ( −2, − 4), Q " (2, − 5), R " ( −1, − 8) c. P " (2, − 4), Q " ( −2, − 5), R " (1, − 8) b. P " ( −2,4), Q " (2,5), R " ( −1,8) d. P " (2, 4), Q " ( −2, 5), R " (1, 8) 5. The vertices of a triangle are P(–7, –4), Q(–7, –8), and R(3, –3). Name the vertices of the image reflected in the line y = x. a. P " (4, 7), Q " (8, 7), R " (3, − 3) c. P " ( −4, − 7), Q " ( −8, − 7), R " ( −3, 3) b. P " (4, − 7), Q " (8, − 7), R " (3, 3) d. P " ( −4, 7), Q " ( −8, 7), R " ( −3, − 3) 6. Which graph shows a triangle and its reflection image in the x-axis?
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Geometry Goncepts I: Final Exam Review
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
In the diagram, the dashed figure is the image of the solid figure.
1. Name the image of ∠E.a. ∠Tb. ∠Qc. ∠Fd. ∠R
2. Name the image of DE.a. TQb. RFc. QRd. FT
3. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of the image reflected in the x-axis.a. P "(3, 8), Q "(6, − 4), R "(−1, 1) c. P "(−3, − 8), Q "(−6, 4), R "(1, − 1)b. P "(−3, 8), Q "(−6, − 4), R "(1, 1) d. P "(3, − 8), Q "(6, 4), R "(−1, − 1)
4. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of the image reflected in the y-axis.a. P "(−2, − 4), Q "(2,− 5), R "(−1,− 8) c. P "(2, − 4), Q "(−2, − 5), R "(1, − 8)b. P "(−2,4), Q "(2,5), R "(−1,8) d. P "(2, 4), Q "(−2, 5), R "(1, 8)
5. The vertices of a triangle are P(–7, –4), Q(–7, –8), and R(3, –3). Name the vertices of the image reflected in the line y = x.a. P "(4, 7), Q "(8, 7), R "(3,− 3) c. P "(−4, − 7), Q "(−8, − 7), R "(−3, 3 )b. P "(4, − 7), Q "(8, − 7), R "(3, 3) d. P "(−4, 7), Q "(−8, 7), R "(−3, − 3)
6. Which graph shows a triangle and its reflection image in the x-axis?
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a.
b.
c.
d.
7. Use an ordered pair to describe the translation that is 6 units to the left and 4 units up.a. 6, − 4
b. −6, 4
c. −6, − 4
d. 6, 4
8. Use an ordered pair to describe the translation that is 7 units to the left and 1 units down.a. −7, − 1
b. 7, 1
c. 7, − 1
d. −7, 1
9. Use an ordered pair to describe the translation that is 8 units to the right and 2 units up.a. −8, − 2
b. 8, 2
c. 8, − 2
d. −8, 2
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10. Use an ordered pair to describe the translation that is 9 units to the right and 6 units down.a. −9, − 6
b. 9, − 6
c. −9, 6
d. 9, 6
Use the diagram.
11. Find the vector that describes the translation B → A.a. 8, 14 b. 7, 2 c. −4, 10 d. 0, 15
12. Find the value of k. The diagram is not to scale. 13. Find the values of x, y, and z. The diagram is not to scale.
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14. Classify the triangle by its sides. The diagram is not to scale.
15. Classify ΔABC by its angles, when m∠A = 32, m∠B = 85, and m∠C = 63.
16. The triangular playground has angles whose measures are in the ratio 8 : 3 : 9. What is the measure of the smallest angle?
17. Find the value of x. The diagram is not to scale.
18. The folding chair has different settings that change the angles formed by its parts. Suppose m∠2 is 26 and m∠3 is 70. Find m∠1. The diagram is not to scale.
19. Find the value of the variable. The diagram is not to scale.
20. Find the value of x. The diagram is not to scale.
Given: ∠SRT ≅ ∠STR, m∠SRT = 20, m∠STU = 4x
21. Classify the polygon by its sides.
22. The chips used in the board game MathFuries have the shape of hexagons. How many sides does each MathFuries chip have?
23. Find the missing angle measures. The diagram is not to scale.
24. If BCDE is congruent to OPQR, then DE is congruent to ? .
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25. In the paper airplane, ABCD ≅ EFGH, m∠B = m∠BCD = 90, and m∠BAD = 131. Find m∠GHE.
26. ∠ABC ≅ ?
27. Given ΔQRS ≅ ΔTUV, QS = 3v + 2, and TV = 7v − 6, find the length of QS and TV.
28. Given ΔABC ≅ ΔPQR, m∠B = 3v + 4, and m∠Q = 8v − 6, find m∠B and m∠Q.
29. State whether ΔABC and ΔAED are congruent. Justify your answer.
30. Name the angle included by the sides PN and NM.
31. From the information in the diagram, can you prove ΔFDG ≅ ΔFDB? Explain.
32. Find the values of x and y.
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33. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?
34. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?
35. Use the information in the figure. Find m∠D.
36. Find the value of x. The diagram is not to scale.
37. Find the value of x. The diagram is not to scale.
Given: RS ≅ ST, m∠RST = 3x − 48, m∠STU = 9x
38. Is there enough information to conclude that the two triangles are congruent? If so, why?
39. The sides of an isosceles triangle have lengths 2x + 4, x + 8. The base has length 5x − 2. What is the length of the base?
40. Find the value of x. The diagram is not to scale.
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41. B is the midpoint of AC, D is the midpoint of CE, and AE = 21. Find BD. The diagram is not to scale.
42. Points B, D, and F are midpoints of the sides of ΔACE. EC = 30 and DF = 23. Find AC. The diagram is not to scale.
43. Find the value of x.
44. Find the length of the midsegment. The diagram is not to scale.
45. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by ∠1 and ∠2 is 11 cm, the side included by ∠2 and ∠3 is 16 cm, and the side included by ∠3 and ∠1 is 14 cm.
46. List the sides in order from shortest to longest. The diagram is not to scale.
47. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side?
48. m∠A = 9x − 7, m∠B = 7x − 9, and m∠C = 28 − 2x. List the sides of ΔABC in order from shortest to longest.
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49. Find the values of the variables and the lengths of the sides of this kite.
50. ABCD is a parallelogram. If m∠CDA = 66, then m∠BCD = ? . The diagram is not to scale.
51. ABCD is a parallelogram. If m∠DAB = 115, then m∠BCD = ? . The diagram is not to scale.
52. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.
53. For the parallelogram, if m∠2 = 5x − 28 and m∠4 = 3x − 10, find m∠3. The diagram is not to scale.
54. Find the values of the variables in the parallelogram. The diagram is not to scale.
55. In the parallelogram, m∠KLO = 68 and m∠MLO = 61. Find ∠KJM. The diagram is not to scale.
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56. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The diagram is not to scale.
57. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
58. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.
59. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
60. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.
Given: XY ≅ WZ and XW ≅ YZ
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61. If ON = 5x − 5, LM = 4x + 4, NM = x − 9, and OL = 2y − 5, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale.
62. If m∠B = m∠D = 41, find m∠C so that quadrilateral ABCD is a parallelogram. The diagram is not to scale.
63. In the rhombus, m∠1 = 15x, m∠2 = x + y, and m∠3 = 30z. Find the value of each variable. The diagram is not to scale.
64. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.
65. Find the values of a and b.The diagram is not to scale.
66. The isosceles trapezoid is part of an isosceles triangle with a 46° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale.
67. Find m∠1 and m∠3 in the kite. The diagram is not to scale.
68. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 20x + 9, and m∠M = 14x + 15, find m∠K.
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69. m∠R = 130 and m∠S = 80. Find m∠T. The diagram is not to scale.
70. m∠R = 110 and m∠S = 100. Find m∠T. The diagram is not to scale.
71. One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78 cm. Find the lengths of the sides of the kite.
ID: A
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Geometry Goncepts I: Final Exam ReviewAnswer Section
MULTIPLE CHOICE
1. D2. C3. C4. C5. C6. D7. B8. A9. B
10. B11. A
SHORT ANSWER
12. 7313. x = 86, y = 67, z = 9414. equilateral15. acute16. 2717. 3318. 9619. 1920. 4021. hexagon22. 623. x = 114, y = 5624. QR25. 4926. ∠MNP27. 828. 1029. yes, by either SSS or SAS30. ∠N31. yes, by ASA32. x = 90, y = 4333. 71°34. 96°35. 32°36. x = 23
ID: A
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37. 1938. Yes; Hypotenuse Leg (HL)39. 1840. 6441. 10.542. 4643. 444. 4245. ∠146. LJ, JK, LK47. less than 2548. AB; AC; BC49. x = 9, y = 13; 11, 2050. 11451. 11552. x = 5, NM = 20, OL = 2053. 16354. x = 29, y = 49, z = 10255. 12956. x = 3, y = 2 57. 458. x = 10, y = 7 59. Yes; opposite angles are congruent.60. Yes; opposite sides are congruent.
61. x = 9, y = 52
62. 13963. x = 6, y = 84, z = 1064. x = 4, DF = 15, EG = 1565. a = 144, b = 6766. 67°; 113°67. 39, 5168. 15169. 7070. 5071. 9.4 cm and 29.6 cm
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