Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Trigonometric functions wikipedia , lookup
Golden ratio wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Renormalization group wikipedia , lookup
Euler angles wikipedia , lookup
History of geometry wikipedia , lookup
LESSON 6.1 Answers for the lesson “Use Similar Polygons” Skill Practice 13. The larger triangle’s perimeter was doubled but should have been halved; perimeter of B 5 14. 1. congruent, proportional 2. Yes; no; if two polygons are congruent, corresponding angles are congruent and the scale factor is 1. If they are similar, corresponding angles are congruent but one polygon can be larger than the other since the scale factor does not have to be 1. 3. A > L, B > M, C > N; AB LM BC MN CA NL Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. F > R, G > S; FG RS 16. sometimes 17. never 18. x: 1; since the order of the figures switched, simply switch the ratio. 19. altitude, 24 GD SP }5}5} 5} 2 1 21. 10 } in., 13 } in. 3 3 areas is approximately equal to the scale factor squared. K >Y, L >Z; JK XY KL YZ 11 23. } 5 26. About 201, 41.6; the ratio of their 5. H > W, J > X, HJ WX 20. median, 9 22 24. AC 5 22 }, ED 5 10 25 3 25. 17 } 5 4. D > P, E > Q, EF QR 15. always 22. 6.4 in. }5}5} DE PQ 14. sometimes 27. No; in similar triangles LH ZW }5}5}5} corresponding angles are congruent. 6. D 2 1 7. similar; RSTU , WXYZ, } 28. D 29. 5 8. similar; nCDE , nTUV, } 4 5 9. } 2 11. 85, 34 10. 27.5, 12, 65 12. 36 in. Geometry Answer Transparencies for Checking Homework 167 30. Yes, yes, yes. Sample answer: nABC , nABC. If nABC , nDEF, then nDEF , nABC. If nABC , nDEF and nDEF , nHJK, then nABC , nHJK. 34. a. 93,000,000 mi B C 432,500 mi A D 240,000 mi E Moon Earth Sun b. Sample answer: Since the Problem Solving triangles are similar, the light from every point of the sun that is in nBDA is blocked by the moon before reaching Earth. 31. No; the side lengths are not proportional. 1 32. yes; } 4 c. about 1116 mi 33. a. 2.8, 4.2, 5.6, 2.1 b. 35. Yes; if * 5 w then the larger and y smaller image would be similar. Sample answer: Let * 5 8, 8 w Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. } w 5 8, and a 5 4; } w 1 a 5 12 2 * *1a 8 2 5 }3 , } 5 } 5 }3. 12 36. The ratio of the areas of similar 1 21 x yes 10 10 c. y 5 }x; }; they are the same. 7 7 figures is the square of the scale factor. Sample answer: Consider two rectangles, one 2 3 4 and the other 6 3 12 with scale factor 8 72 1 3 1 9 } and ratio of areas } 5 }, 1 2 1 3 } 2 1 5 }9. Geometry Answer Transparencies for Checking Homework 168 37. a. They have the same slope. b. b, c; BOA > DOC by the Vertical Angles Theorem; OBA > ODC by the Alternate Interior Angles Theorem; BAO > DCO by the Alternate Interior Angles Theorem. } 1 1 Ï5 } } 1 1 Ï5 2 39. }; } 2 1 1 5} } 1 1 Ï5 }21 2 c. A(23, 0), B(0, 4), C(6, 0), D(0, 28); AO 5 3, OB 5 4, BA 5 5, CO 5 6, OD 5 8, DC 5 10 38. L M b c a Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. K Q d N bx cx ax P R dx S Sample answer: KLMN , PQRS is given. Since the rectangles are x similar, let }1 be the scale factor and let a, b, c, d be the lengths of the sides of KLMN and ax, bx, cx, dx be the lengths of the corresponding sides of PQRS. Taking the ratio of perimeters ax 1 bx 1 cx 1 dx a1b1c1d x(a 1 b 1 c 1 d) }} 5 x. a1b1c1d you get }} 5 Geometry Answer Transparencies for Checking Homework 169