8.2 Polygons 469 x ft 45 ft 9 ft 6 ft Figure 8.22 Solution We will let x represent the height of the tree. From Fig. 8.22, we can see that the triangle formed by the sun’s rays, Allisha and her shadow is similar to the triangle formed by the sun’s rays, the tree, and its shadow. To determine the height of the tree, we will set up and solve the following proportion: = = = = x x x height of the tree height of Allisha length of tree’s shadow length of Allisha’s shadow 6 45 9 9 270 30 Therefore, the tree is 30 ft tall. 7 Now try Exercise 75 Congruent Figures If the corresponding sides of two similar figures are the same length, the figures are called congruent figures. Corresponding angles of congruent figures have the same measure, and the corresponding sides are equal in length. Two congruent figures coincide when placed one upon the other. A B B9 C9 A9 C 21.2 26 24 508 608 Figure 8.23 Example 4 Congruent Triangles Triangles ABC and ′ ′ ′ A BC in Fig. 8.23 are congruent. Determine a) the length of side ′ ′ AC . b) the length of side AB. c) ′ ′ ′ m C A B. d) m ACB. e) m ABC. Solution Because ΔABC is congruent to Δ ′ ′ ′ A BC , we know that the corresponding side lengths are equal and corresponding angle measures are equal. a) ′ ′ = = AC AC 26 b) = ′ ′ = AB A B 21.2 c) ′ ′ ′ = = m C A B m CAB 60° d) = ′ ′ ′ = m ACB m AC B 50° e) The sum of the angles of a triangle is ° 180 . Since = m BAC 60° and = = − − = m ACB m ABC 50°, 180° 60° 50° 70°. 7 Now try Exercise 63
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