Exercise 25 Page 613

We know that the vertex angles of each triangle are congruent. Let's mark this in the diagram. Note that we will dim the colors somewhat to make it clearer.

What can we can about the yellow triangle and the yellow-orange triangle? Well, for one they have congruent vertex angles. Second, they share a side. Therefore, by the Reflexive Property of Congruence we know that these sides are congruent.

However, both the yellow triangle and the yellow-orange triangle are isosceles. Therefore, the second leg in each of the triangles are congruent with the first leg.

Now we can continue using the fact that each of the triangles are isosceles and mark all of these sides as congruent.

Since two sides and its included angle are congruent in the yellow and purple triangle, we know they are congruent by the SAS Congruence Theorem.