Geometry Midterm REVIEW

Transcription

1 Class: Date: Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. 1. How are 6 and 2 related? a. corresponding angles c. same-side interior angles b. alternate interior angles d. none of these 2. What is the graph of 2x 4y = 8? a. b. c. d. 3. Write an equation in point-slope form of the line through point J(2, 9) with slope 9. a. y 9 = 9 ( x 2) b. y 9 = 9 ( x 2) c. y 9 = 9 ( x + 2) d. y + 9 = 9 ( x + 2) 4. Write an equation in slope-intercept form of the line through points S( 9, 3) and T( 1,7). a. y = 5 4 x + 33 b. y = x + 33 c. y = x 33 d. y = x

2 5. Name the theorem or postulate that lets you immediately conclude ΔABD ΔCBD. a. AAS b. ASA c. SAS d. none of these 6. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent? a. either SAS or AAS c. SAS only b. AAS only d. neither 7. Which of these transformations are isometries? (I) parallelogram EFGH parallelogram XWVU (II) hexagon CDEFGH hexagon YXWVUT (III) triangle EFG triangle VWU a. I only b. II and III only c. I and III only d. I, II, and III 8. Which letter has at least one line of symmetry? a. H b. G c. J d. F 9. Which letter has rotational symmetry? a. R b. J c. B d. I 2

3 10. Which image has reflectional, rotational, and point symmetry? a. b. c. d. 11. Which type of isometry is the equivalent of two reflections across intersecting lines? a. glide reflection b. rotation c. reflection d. none of these 12. Find the glide reflection image of the black triangle where the translation is (x,y) (x 8,y 7) and line of reflection is x = 3. a. b. c. d. Short Answer 13. Name the plane represented by the top of the box. 14. Name the intersection of plane BPQ and plane CPQ. 15. What is the intersection of plane YZVU and plane ZWSV? 3

4 16. What is the length of BD? 17. If EF = 3x 11, FG = 4x 8, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale. 18. If Z is the midpoint of RT, what are x, RZ, and RT? 19. If m AOC = 67, m BOC = 2x + 10, and m AOB = 4x 15, find the degree measure of BOC and AOB. The diagram is not to scale. 20. If m DEF = 118, then what are m FEG and m HEG? The diagram is not to scale. 4

5 21. Name an angle adjacent to DGE. 22. The complement of an angle is 54. What is the measure of the angle? and 2 are a linear pair. m 1 = x 14, and m 2 = x Find the measure of each angle. 24. MO bisects LMN, m LMO = 8x 27, and m NMO = 2x Solve for x and find m LMN. The diagram is not to scale. 25. Which point is the midpoint of AB? 26. Find the coordinates of the midpoint of the segment whose endpoints are H(6, 3) and K(2, 15). 27. M(7, 3) is the midpoint of RS. The coordinates of S are (8, 2). What are the coordinates of R? 28. Find the distance between points P(2, 4) and Q(8, 6) to the nearest tenth. 29. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square. 5

6 Use the diagram to find the following. 30. Identify a pair of same-side interior angles. 31. What are three pairs of corresponding angles? 32. What is the relationship between 3 and 7? This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. 33. If 8 measures 110, what is the sum of the measures of 1 and 4? 6

7 34. Find m P. The diagram is not to scale. 35. Find the value of x. The diagram is not to scale. 36. Find the value of x for which l is parallel to m. The diagram is not to scale. 37. Find the value of k. The diagram is not to scale. 7

8 38. Find the values of x, y, and z. The diagram is not to scale. 39. What is the slope of the line shown? 40. What is an equation in point-slope form for the line perpendicular to y = 2x 13 that contains (9, 5)? 41. If BCDE is congruent to OPQR, then DE is congruent to?. 42. NPM? 8

9 43. The two triangles are congruent as suggested by their appearance. Find the value of f. The diagrams are not to scale. 44. Justify the last two steps of the proof. Given: PQ SR and PR SQ Prove: ΔPQR ΔSRQ Proof: 1. PQ SR 1. Given 2. PR SQ 2. Given 3. QR RQ 3.? 4. ΔPQR ΔSRQ 4.? 9

10 45. Which triangles are congruent by ASA? 46. What is the value of x? 47. What is the value of x? 10

11 48. Find the values of x and y. In the diagram, figure RQTS is the image of figure DEFC. 49. Name the image of E. 50. Name the image of FC. 51. What image is the translation of the shown triangle given by the translation rule (x, y) (x 3, y + 3)? 11

12 52. What image is the translation of ABC given by the translation rule (x, y) (x 3, y 3)? Use the diagram. 53. Find the image of C under the translation described by the translation rule (x, y) (x + 4, y 10). 54. Use a translation rule to describe the translation that is 9 units to the left and 6 units up. 55. What is a rule that describes the translation ABCD Aʹ Bʹ C ʹ Dʹ? 12

13 56. What translation rule can be used to describe the result of the composition of (x, y) (x + 9, y 1) and (x, y) (x 5, y 5)? 57. Write a rule to describe the transformation that is a reflection across the y-axis. 58. The vertices of a triangle are P(5, 8), Q(2, 6), and R( 4, 1). Name the vertices of the image reflected across the line y = x. 59. Find the image of O(2, 2) after two reflections, first across the line y = 3, and then across the line x = 1. The hexagon GIKMPR and ΔFJN are regular. The dashed line segments form 30 angles. 60. Find the image of ON after a rotation of 120 about point O. 61. Find the angle of rotation about O that maps H to F. 62. Find the degree of rotation about the spinner center that maps label i to label D. 13

14 63. How many lines of symmetry does the figure have? 64. Name the type of symmetry for the figure. 65. Name the translation image of ΔABC after a reflection across line t and then a reflection across line r. 14

15 Geometry Midterm REVIEW Answer Section MULTIPLE CHOICE 1. A 2. A 3. B 4. A 5. A 6. B 7. D 8. A 9. D 10. D 11. B 12. D SHORT ANSWER 13. ACD 14. PQ 15. VZ x = 6, EF = 7, FG = x = 13, RZ = 103, and RT = m BOC = 34 ; m AOB = m FEG = 62, m HEG = EGH = 51, 2 = x = 10, m LMN = (4, 9) 27. (6, 4) blocks and angles 3 & 5, 1 & 7, and 8 & corresponding angles º

16 x = 79, y = 66, z = y + 5 = 1 (x 9) QR 42. BCA Reflexive Property of ; SSS 45. ΔVTU and ΔHGF x = 90, y = R 50. FT B 2

17 54. (x, y) (x 9, y + 6) 55. (x, y) (x 2, y 3) 56. (x, y) (x + 4, y 6) 57. (x, y) ( x, y) 58. Pʹ (8, 5), Qʹ (6, 2), Rʹ ( 1, 4 ) 59. ( 4, 8) 60. OJ rotational 65. ΔUVW 3