If two triangles are similar, then the lengths of their corresponding angle bisectors are proportional to the lengths of their corresponding sides.
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Practice makes perfect
Let's analyze the given triangles.
First, notice that two angles of the bigger triangle are congruent to two angles of the smaller triangle. Therefore, by the Angle-Angle Similarity Theorem, these triangles are similar.
â–³_(Bigger) ~ â–³_(Smaller)
We are given the lengths of the corresponding sides of the triangles. Recall that if two triangles are similar, the lengths of their corresponding angle bisectors are proportional to the lengths of their corresponding sides. Therefore, we can write the following proportion.
21/6 = x/8
Let's solve it!
