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LESSON 4.9 Answers for the lesson “Perform Congruence Transformations” Skill Practice 11. y 1. Subtract 1 from each x-coordinate and add 4 to each y-coordinate. 1 2. The image is congruent to 21 the original figure. 3. translation 4. rotation 5. reflection 6. yes 7. no 8. yes 9. x 12. y y 1 1 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 21 x 21 x 13. (x, y) l (x 2 4, y 2 2) 14. (x, y) l (x 1 6, y 1 3) y 10. 15. (x, y) l (x 1 2, y 2 1) 1 21 x 16. (x, y) l (x 2 7, y 1 9) 17. y 1 21 x Geometry Answer Transparencies for Checking Homework 129 18. y 21. y C 1 1 21 D 21 x x B A 19. y not a rotation 22. 1 21 y D x C 1 A 21 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 20. y 1 21 x B B A not a rotation x C y 23. A D rotation; 908 clockwise 1 21 C B x D not a rotation Geometry Answer Transparencies for Checking Homework 130 24. The red triangle rotation segment 40. a. Sample answer: MOM, TOT should connect corresponding angles of the triangle; the red triangle is rotated 908 clockwise. 25. Yes; take any point or any line segment and rotate 3608. MOM b. Sample answer: HI, OH HI y P 3 360 3 TOT OH 41. a. (x, y) l (x 2 1, y 1 2) x 360 b. (x, y) l (x 1 2, y 2 1) c. No; the translation needed does Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. not match a knight’s move. 26. (2, 2) 27. (3, 4) 28. (21, 0) 29. (2, 3) 30. (3, 5) 31. (13, 25) 32. The corresponding sides of each triangle are congruent therefore the triangles are congruent. 33. } UV 34. } AV 35. nDST 36. n XYC 37. m 5 3, n 5 11, a 5 2, 1 g 5 2, h 5 }4 Problem Solving 38. a. The designer can reflect the layout over the horizontal line. b. 4 ft } and EF } are 42. The slopes of BC both 21 and the slopes of } and DE } are both 1. Therefore, AB }> } AB BC since the product of their slopes is 21. Similarly, } > EF }. Thus n ABC and DE n DEF are right triangles. Using the distance formula, } BC 5 EF 5 Ï2}and AC 5 DF 5 Ï10 . So, } > EF } > DF }, AC }. By the HL BC Congruence Theorem, n ABC > n DEF. Therefore, n DEF is a congruence transformation of n ABC, described by the notation (x, y) l (x 2 5, y 1 1). 43. B 39. 908 clockwise, 908 counterclockwise Geometry Answer Transparencies for Checking Homework 131 44. (1, 4), (1, 1), (3, 1); no; the final 5. a. In n ABC, it is given that } AB > } CB, therefore image would have a different rotation segment. Mixed Review of Problem Solving BCE > BAE by the Base Angles Theorem. b. Sample answer: n ABE > nCBE by AAS. } CE > } AE by corr. parts of s are > . n FAE > n DCE >n by ASA and therefore } AF > } CD by corr. parts of > s are >. n 1. a. reflection in the y-axis b. rotation of 908 counterclockwise c. reflection in the x-axis d. Rotate figure A 908 clockwise and 1808. 6. 7; 7 2. No; the given angle is not the included angle. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 3. The length of the side forming the 348 angle with side measuring 8 centimeters, the angle the third side makes with the side measuring 8 centimeters, or the angle the third side makes with the side forming the 348 angle with the side measuring 8 centimeters 4. Yes; yes; ACD and BCE are vertical angles so they are congruent which makes n ACD > n BCE by SAS. Since } > BE } by n ACD > n BCE, AD s are > . corr. parts of > n Geometry Answer Transparencies for Checking Homework 132