8.2 Polygons 473 52. y x 27 12 15 A B E D F C 36 Ac Bc Ec Dc Cc Fc = = x y 16, 20 In Exercises 53–56, triangles ABC and DEC are similar figures. Determine the length of 3 5 1 1 A B C E D 53. side BC. 3 54. side DC. 12 3 55. side AD. 31 3 56. side BE. 2 In Exercises 57– 62, determine the length of the sides and the measures of the angles for the congruent triangles ABC and ′ ′ ′ A BC. 18 33 34 A C B 788 318 C9 B9 A9 57. The length of side AB 33 58. The length of side ′ ′ AC 59. The length of side ′ ′ BC 60. m ABC 78° 61. m ACB 71° 62. ′ ′ ′ m AC B 71° In Exercises 63– 68, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and ′ ′ ′ ′ A BC D. A 10 B D 130 11 8 708 C C' 508 D' B' A' 9 63. The length of side AD 9 64. The length of side ′ ′ BC 11 65. The length of side ′ ′ A B 10 66. m BCD ° 50 67. m DAB ° 110 68. ′ ′ ′ m A DC ° 70 34 18 69. Rhombus ABCD is shown below. a) Determine the measure of interior angle x. ° 85 b) Determine the measure of exterior angle y. ° 95 A B y x 958 C D 70. Parallelogram ABCD is shown below. a) Determine the measure of interior angle x. ° 97 b) Determine the measure of exterior angle y. ° 83 y x 978 Problem Solving 71. Distances in Texas A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Austin, Houston, and San Antonio (see the following figure). If the actual distance from Austin to Houston is approximately 160 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate a) the actual distance from Austin to San Antonio. 80 miles b) the actual distance from San Antonio to Houston. 200 miles Austin 2 in. 1 in. Houston 2.5 in. San Antonio Area of detail 72. Distances in Missouri A triangle can be formed by drawing line segments on a map of Missouri connecting the cities of Kansas City, Springfield, and St. Louis (see the following figure). If the actual distance from Kansas City to St. Louis is approximately 248 miles, use the *See Instructor Answer Appendix
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