A18 APPENDIX Review Figure 21 6 3 5 B A C x 305 605 905 Figure 19 Similar triangles a b c 30 30 70 70 80 80 d = 2a e = 2b f = 2c It is not necessary to verify that all three angles are equal and all three sides are proportional to determine whether two triangles are similar. Figure 20 355 355 1205 10 30 5 15 18 12 4 18 6 6 805 805 (a) (b) (c) 1205 Determining Similar Triangles • Angle–Angle Case Two triangles are similar if two of the corresponding angles are equal. For example, in Figure 20(a), the two triangles are similar because two angles are equal. • Side–Side–Side Case Two triangles are similar if the lengths of all three sides of each triangle are proportional. For example, in Figure 20(b), the two triangles are similar because 10 30 5 15 6 18 1 3 = = = • Side–Angle–Side Case Two triangles are similar if two corresponding sides are proportional and the angles between the two sides are equal. For example, in Figure 20(c), the two triangles are similar because 4 6 12 18 2 3 = = and the angles between the sides are equal. Using Similar Triangles Given that the triangles in Figure 21 are similar, find the missing length x and the angles A , B , and C . EXAMPLE 5
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