If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Notice that ∠ A and ∠ C are congruent angles, and ∠ AEB and ∠ CED are also congruent angles. This means that two angles of △ ABE are congruent to two angles of △ CDE. Therefore, by the Angle-Angle Similarity Theorem, △ ABE and △ CDE are similar triangles.
△ ABE ~ △ CDE
Finding the Measure
Using our similarity statement from above, we can identify two pairs of corresponding sides that will help us find the requested length.
AB corresponds with CD
EA corresponds with EC
Recall that corresponding sides of similar figures will have proportional lengths. We are given expressions for the lengths of these sides, which we can use to write a proportion.
AB/CD = EA/EC
⇓
x/10 = 5/8
Let's solve the above equation for x.
