7.2.1 Applying Properties of Similar Triangles (continued) Example 4 Using the Triangle Angle Bisector Theorem An angle bisector of a triangle divides the
opposite side into two segments whose lengths are proportional to the lengths of the other two sides.
The lengths of two line segments are determined using the Triangle Angle Bisector Theorem. The lengths of the unknown segments are given as algebraic expressions of an unknown, x . The lengths of the other two sides of the triangle are given. Given BD bisects ∠ ADC , write a proportion that correctly relates the ratio of the lengths of the two line segments formed by the bisector to the ratio of the lengths of the other two sides. Substitute the given values into the proportion, cross multiply, and solve for the unknown, x . The solution yields x = 7. To obtain the answer to the example, the lengths of the line segments AB and BC , substitute 7 into the equations for their lengths. This gives AB = 8 and BC = 10.
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