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Name: ________________________ Class: ___________________ Date: __________ 2nd Nine Weeks Extra Credit (Unit 2) Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. If a. b. c. d. ____ DEF , which segment is congruent to AC ? DF AB EF DE 2. Triangle ABC is similar to triangle DEF. What is the value of x ? a. b. ____ ABC 20 15 c. d. 30 60 3. In the figure, quadrilateral RSTU quadrilateral HIFG. Find b. a. b. b = 75 b=5 c. d. 1 b = 98 b = 70 ID: B Name: ________________________ ____ ID: B 4. Which describes the transformation from the original to the image, and tells whether the two figures are similar or congruent? a. b. dilation, similar rotation, congruent c. d. translation, congruent rotation, similar ____ 5. Translate the quadrilateral W 2,2 , X 3,3 , Y 6,5 , Z 6,3 using the transformation x 2,y 3 . a. W' 0,5 , X' 1,6 , Y' 4,8 , Z' 4,6 b. W' 4,5 , X' 5,6 , Y' 8,8 , Z' 8,6 c. W' 0, 1 , X' 1,0 , Y' 4,2 , Z' 4,0 d. W' 4,6 , X' 6,9 , Y' 12,15 , Z' 12,9 ____ 6. Describe the transformation M: x, y x, y . a. A reflection across the x-axis. b. A dilation with a scale factor 1 and center 0, 0 . c. A rotation 180 with center of rotation 0, 0 . d. A translation one unit down and one unit to the right. 2 Name: ________________________ ____ 7. In the figure, 6 and 2 are _____________. a. b. ____ consecutive interior angles corresponding angles c. d. alternate exterior angles alternate interior angles 8. At the same time of day, a man who is 76 inches tall casts a 57-inch shadow and his son casts a 24-inch shadow. What is the height of the man's son? (Figures may not be drawn to scale.) a. ____ ID: B 108 in. b. 33 in. c. 32 in. d. 9. What is the image of 8,1 when it is reflected across the line y x ? 1 a. 1,8 c. ,1 8 1 b. 1,8 d. 1, 8 ____ 10. Which mapping represents a rotation of 270 clockwise about the origin? a. x,y y, x c. x,y x,y b. x,y y,x d. x,y x, y 3 81 in. Name: ________________________ ID: B ____ 11. In the figure, 6 and 3 are __________. a. b. corresponding angles alternate exterior angles c. d. consecutive interior angles alternate interior angles ____ 12. A triangle has vertices (4, 1), (3, 0), and (7, 2). What are the vertices of the image of the triangle after a reflection across the y-axis? a. (4, 1), (3, 0), and (7, 2) b. (1, 4), (0, 3), and (2, 7) c. (4, 1), (3, 0), and (7, 2) d. (4, 1), (3, 0), and (7, 2) ____ 13. The postulate or theorem that can be used to prove that the two triangles are similar is _____. a. b. SSS Similarity ASA Congruence c. d. SAS Similarity AA Similarity ____ 14. If the two triangles are congruent, what is the length of x? a. b. 12 14 c. d. 4 28 16 Name: ________________________ ID: B ____ 15. Which of the following proportions could be used as a given to show that AB DF ? a. b. c. d. DE DF EF DF DA AE DA BE AE AB EB AB FB BE AE BE ____ 16. In the figure below, A D and B E . To show that ABC DEF , you can apply a dilation to ABC so that the image is congruent to DEF . What is the scale factor of the dilation? a. b. c. d. BC EF AD BE AB DE DF AC 5 Name: ________________________ ID: B ____ 17. Given a triangle with vertices A 4, 1 , B 3, 0 , and C 7, 2 , which points represent a reflection of ABC in the y-axis? a. A 1, 4 , B 0, 3 , C 2, 7 c. A 4, 1 , B 3, 0 , C 7, 2 b. A 4, 1 , B 3, 0 , C 7, 2 d. A 4, 1 , B 3, 0 , C 7, 2 ____ 18. What information is needed to prove a. b. MLK KM 10 KL 10 PQR by SAS? c. d. KM 9.5 KL 9.5 c. d. AOC COD ____ 19. Name an angle supplementary to AOE . a. b. AOB BOC ____ 20. What is the image of the point 10,6 after a 90 counterclockwise rotation? a. 10,6 c. 6, 10 b. 10, 6 d. 6,10 6 Name: ________________________ ID: B ____ 21. For two triangles with identical orientation, what rigid motion is necessary for SAS congruence to be shown? a. b. Dilation Rotation c. d. Translation Reflection ____ 22. Which sequence of transformations shows that figures A and B are congruent? a. b. c. d. Rotate figure A 90 clockwise about the origin and then translate right 5 units. Rotate figure A 90 counterclockwise about the origin and then translate down 5 units. Reflect figure A across the x-axis and then translate right 6 units and up 1 unit. Reflect figure A across the y-axis and then translate right 1 unit and up 4 units. ____ 23. Refer to the figure shown. Which of the following statements is true? a. b. TUV WXV by SAS TUV WXV by SSS c. d. 7 TUV VWX by SAS TUV XWV by ASA Name: ________________________ ID: B ____ 24. If two polygons are SIMILAR, then the corresponding sides must be _____. a. proportional c. parallel b. similar d. congruent ____ 25. Prove that the triangles with the given vertices are congruent. A(3, 1), B(4, 5), C(2, 3) D(–1, –3), E(–5, –4), F(–3, –2) a. The triangles are congruent because ABC can be mapped onto DEF (x,y) (x,y), followed by a rotation: (x,y) (y,x). b. The triangles are congruent because ABC can be mapped onto DEF (x,y) (y,x), followed by a reflection: (x,y) (x,y). c. The triangles are congruent because ABC can be mapped onto DEF (x,y) (x 4,y), followed by another translation: (x,y) (x,y 6). d. The triangles are congruent because ABC can be mapped onto DEF (x,y) (y,x), followed by a reflection: (x,y) (x,y). ABC ____ 26. a. b. 29 87 b. c. d. by a rotation: by a translation: by a rotation: EDF . Find f. c. d. 58 35 ____ 27. What is the best first step when finding a sequence of rigid motions to map a. by a reflection: ABC to DEF ? Find a single transformation that maps one vertex of ABC to the corresponding vertex of EFD. Find a single transformation that maps one vertex of ABC to the corresponding vertex of DEF . Find a single transformation that maps one angle of ABC to the corresponding angle of another triangle AB C . Find a single transformation that maps one side of ABC to the corresponding side of DEF . 8 Name: ________________________ ID: B ____ 28. Which describes the transformation from the original to the image, and tells whether the two figures are similar or congruent? a. b. translation, congruent translation, similar c. d. reflection, congruent dilation, similar ____ 29. Which is the image of 4,7 rotated 180 about the origin? a. 4,7 c. 7,4 b. 7,4 d. 4,7 ____ 30. ABC and DEF have the following properties: AB DE , BC EF , and B E . If AB = 18, BC = 13, and mB = 45, and DE = n + 12, EF = 3n – 5, and mE = (5n + 15)°, determine the value of n. a. n = 11 c. n = 9 b. n = 6 d. n = 13 9 Name: ________________________ ID: B ____ 31. This drawing illustrates ______. a. b. SSS Similarity SAS Similarity c. d. AA Similarity SAS Congruence c. d. x 9.75 y 10.2 x 8.75 y 11.2 ____ 32. Given that ABC DEF solve for x and y. a. b. ____ 33. If a. b. c. d. x 9.75 y 11.2 x 8.75 y 10.2 ABC GHI , what is the length of GH ? 13 10 23 The length cannot be determined. 10 Name: ________________________ ID: B ____ 34. What single rigid motion can move the solid figure onto the dashed figure? a. b. dilation translation c. d. reflection rotation ____ 35. Figure A is congruent to figure B. What sequence of transformations maps figure A to figure B? a. b. c. d. (x, y) (x, y 2) followed by (x, y) (x, y) (x, y) (x, y 2) followed by (x, y) (x, y) (x, y) (x, y) followed by (x, y) (x, y 2) (x, y) (x, y) followed by (x, y) (x, y 2) 11 Name: ________________________ ID: B ____ 36. Write a congruence statement for the pair of congruent polygons. a. b. c. d. Quadrilateral EFGH quadrilateral MNKL Quadrilateral EFGH quadrilateral NKLM. Quadrilateral EFGH quadrilateral KLMN Quadrilateral EFGH quadrilateral LMNK ____ 37. Which coordinate notation correctly describes a transformation that maps the black triangle to the gray triangle? a. b. c. d. The translation x, y x 4, y 8 The rotation x, y y, x The rotation x, y x, y The translation x, y x 6, y 2 12 Name: ________________________ ID: B ____ 38. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. D: (x,y) (0.5x,0.5y) J(1, 4), K(6, 4), L(6, 1), M(1, 1) a. b. J´(0.5, 2), K´(3, 2), L´(6, 1), M´(1, 1) J´(2, 0.5), K´(2, 3), L´(0.5, 3), M´(0.5, 0.5) c. d. J´(–0.5, –2), K´(–3, –2), L´(–3, –0.5), M´(–0.5, –0.5) J´(0.5, 2), K´(3, 2), L´(3, 0.5), M´(0.5, 0.5) ____ 39. Which describes the transformation from the original to the image, and tells whether the two figures are similar or congruent? a. b. reflection, congruent translation, similar c. d. translation, congruent dilation, similar ____ 40. One way to show that two triangles are similar is to show that ______. a. an angle of one is congruent to an angle of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. two angles of one are congruent to two angles of the other 13 Name: ________________________ ID: B ____ 41. If line m line n and 2 measures 35, what is the measure of 5? a. b. 55 145 c. d. 155 180 c. d. 4 8.5 ____ 42. ABCD LMNO. What is the value of r? a. b. 9 6.5 ____ 43. Obtuse triangle ABC obtuse triangle DEF. mA = 104 and mF = 32. Find mB. a. 32 c. 44 b. 42 d. 104 ____ 44. Given AB DE , B E , and BC EF , which is a good first step when proving that a. b. c. d. Translate ABC so it maps onto DEF . Find a sequence of rigid motions that maps AB onto DE . Find a sequence of rigid motions that maps A onto F . Find a sequence of rigid motions that maps AB onto BC . 14 ABC DEF ? Name: ________________________ ____ 45. Determine whether triangles a. b. c. d. ID: B EFG and The triangles are congruent because (x,y) (y,x). The triangles are congruent because (x,y) (x,y). The triangles are congruent because (x,y) (x,y). The triangles are congruent because (x,y) (y,x). PQR are congruent. EFG can be mapped to PQR by a rotation: EFG can be mapped to PQR by a reflection: EFG can be mapped to PQR by a reflection: EFG can be mapped to PQR by a rotation: 15 Name: ________________________ ____ 46. ID: B JKL is translated using (x,y) x 1,y 3 after it is reflected across the x-axis. What are the coordinates of the final image of point J under this composition of transformations? a. b. 6, 1 1,6 c. d. 6,1 1, 6 ____ 47. The transformation: x, y x 5, y 7 is a __________. a. Reflection b. Dilation c. Translation d. Rotation ____ 48. When the point 3,2 is reflected across the y-axis, what is the resulting image? a. 3, 2 c. 3, 2 b. 3,2 d. 2, 3 16 Name: ________________________ ID: B ____ 49. Are rectangles ABCD and WXYZ congruent? If so, what is a sequence of transformations that maps ABCD to WXYZ ? a. b. c. d. Yes; reflect across the x-axis and then translate 8 units left. Yes; reflect across the y-axis and then rotate 90 counterclockwise about the origin. Yes; rotate 90 clockwise about the origin and then translate 8 units left. No; there is no sequence of transformations that maps ABCD to WXYZ. ____ 50. A figure lies in Quadrant II of a coordinate plane. The figure is transformed by first reflecting across the x-axis and then rotating 90 clockwise about the origin. In what quadrant will the image lie? a. b. c. d. Quadrant I Quadrant II Quadrant III Quadrant IV 17