Prove: If the base angles of a triangle are congruent, then the triangle is isosceles.?

Ideas: Draw the height first. You can prove that the two triangles are similar because of AA~. Since the height is the common part of two triangles, by ASA, the two triangles are congruent. Therefore the two sides are congruent (CPCTC). In this way, you proved that the original triangle is an isosceles triangle.