Pre-Calculus Homework Solutions 92

Pre-Calculus Homework Solutions 92 - 6. The red triangles...

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Unformatted text preview: 6. The red triangles are congruent: BME, ANG, DKH, CLF. The blue triangles are congruent: EMJ, GNJ, HKJ, FLJ. The purple triangles are congruent to each other and to the triangles made up of a blue triangle and a red triangle: BLJ, AMJ, JND, JKC, BMJ, ANJ, JKD, JLC. Another set of congruent triangles consists of triangles made up of a red, a blue, and a purple triangle: BAJ, ADJ, DCJ, CBJ. Another set of congruent triangles consists of the triangles which are each half of the square: BCD, ADC, CBA, DAB. 7. y 36 3 2 13 9 3 or 30 13 13 y y 6 The point of intersection is 13 , 30 . 13 Then, use the Distance Formula to determine the 6 distance between (0, 3) and 13 , 30 . 13 d ¬ (x2 6 13 ¬ 36 ¬ 169 x1)2 0 2 (y2 30 13 y1)2 3 2 81 169 117 ¬ 117 or 13 169 The distance between the lines is 56. 2y 142 ¬180 linear pair 150 ¬180 2y ¬30 y ¬15 4x 6 ¬142 corresponding angles 4x ¬136 x ¬34 z ¬4x 6 alternate exterior angles z ¬4(34) 6 z ¬142 57. x 68 ¬180 supplementary consecutive interior angles x ¬112 4y 68 ¬180 linear pair 4y ¬112 y ¬28 5z 2 ¬x alternate interior angles 5z 2 ¬112 5z ¬110 z ¬22 58. 3x ¬48 alternate interior angles x ¬16 y 42 48 ¬180 Angle Sum Theorem y 90 ¬180 y ¬90 z 42 alternate interior angles 59. reflexive 60. symmetric 61. symmetric 62. transitive 63. transitive 64. transitive 8 2y 4-3 x R Congruent Triangles 9. 11. 13. 14. 15. 16. Chapter 4 4. Z HJT J, WX T’ R’ Pages 195–198 Practice and Apply 1. The sides and the angles of the triangle are not affected by a congruence transformation, so congruence is preserved. 2. Sample answer: AFC DFB W S, X T, XZ TJ, WZ SJ T Use the Distance Formula to find the length of each side in the triangles. QR ¬ [ 4 ( 4)]2 ( 2 3)2 ¬ 0 25 or 5 Q R ¬ (4 4)2 ( 2 3)2 ¬ 0 25 or 5 RT ¬ [ 1 ( 4)]2 [ 2 ( 2)]2 ¬ 9 0 or 3 R T ¬ (1 4)2 [ 2 ( 2)]2 ¬ 9 0 or 3 QT ¬ [ 1 ( 4)]2 ( 2 3)2 ¬ 9 25 or 34 Q T ¬ (1 4)2 ( 2 3)2 ¬ 9 25 or 34 The lengths of the corresponding sides of two triangles are equal. Therefore, by the definition of congruence, QR Q R , RT R T , and QT Q T . Use a protractor to measure the angles of the triangles. You will find that the measures are the same. In conclusion, because QR Q R , RT R T , QT Q T , Q Q, R R , and T T , QRT QRT. Q R T is a flip of QRT. 8. G K, H L, J P, GH KL, HJ LP, GJ KP Page 195 Check for Understanding 3. 5. Q’ Q 117 13 units. 17. TKH ST, 18. 94 CFH JKL 10. RSV TSV WPZ QVS 12. EFH GHF T X, U Y, V Z, TU XY, UV YZ, TV XZ C R, D S, G W, CD RS, DG SW, CG RW B D, C G, F H, BC DG, CF GH, BF DH A H, D K, G L, AD HK, DG KL, AG HL 1 10, 2 9, 3 8, 4 7, 5 6 s 1–4, s 5–12, s 13–20 ...
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