Pre-Calculus Homework Solutions 185

# Pre-Calculus Homework Solutions 185 - 9 Using corresponding...

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9. Using corresponding angles, MAD MCB . C AM M x 25 20 1 3 2 x 300 3 x 2 60 x 0 3 x 2 60 x 300 0 x 2 20 x 100 0 ( x 10)( x 10) x 10 0 x 10 The scale factor is D BM M 1 3 2 x 3( 12 10) 3 1 0 2 or 5 : 2. 10. M PQ L 1 5 0 or 1 2 M PR N 1 6 2 or 1 2 Q LN R 3 6 or 1 2 Corresponding sides are proportional, so the triangles are similar by SSS Similarity. 11. PTS QTR since they are vertical angles. m PTS m QTR 90. m PTS m S m P 180 90 62 m P 180 m P 28 m QTR m R m Q 180 90 66 m Q 180 m Q 24 Since only one pair of corresponding angles is congruent, the triangles are not similar. 12. ED CB so AED ACB and ADE ABC because corresponding angles are congruent. Then the triangles are similar by AA Similarity. 13. G K K J G H H I 8 KJ KJ 1 4 2 4(8 KJ ) 12( KJ ) 32 4( KJ ) 12( KJ ) 32 16( KJ ) 2 KJ 14. G K K J G H H I G 6 K 14 7 7 G 6 K 7 7 7( GK ) 42 GK 6 15. G K K J G H H I 6 4 H 9 I 6( HI ) 36 HI 6 GI GH HI 9 6 or 15 16. Let x represent the perimeter of DEF . C E B F 1 1 0 4 7 10 x 13 1 1 0 4 3 x 0 10 x 420 x 42 The perimeter of DEF is 42 units. 17. CMA ACB and A A , so ABC ACM by AA Similarity. ( AM ) 2 6 2 10 2 ( AM ) 2 36 100 ( AM ) 2 64 AM 8 C B M C A A M C B 6 C 1 8 0 8( BC ) 60 BC 7.5 C B M C ¬ A A B C 7 6 .5 ¬ 8 10 MB 75 ¬4 48 6( MB ) 27 ¬ 6( MB ) 4.5 ¬ MB The perimeter of ABC is 10 7.5 8 4.5 or 30. 18. 19. 4 x ft ¬ 2 6 0 5 i i n n . . 4 x 8 ¬ 2 6 0 5 3120 ¬ 20 x 156 ¬ x The height of the top of the backboard is
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