Isosceles Triangle Theorem Proof?

Question

Can someone tell me what the two column proof is for the Isosceles Triangle Theorem and if possible its converse?

Answer 1

There are several isosceles triangle theorems. They involve the median, angle bisector and altitude to the base. The following link covers it all well:

http://planetmath.org/encyclopedia/IsoscelesTriangleTheorem.html

Answer 2

There are quite a few theorems concerning isosceles triangles. Their proofs in many situations use acceptable triangles shaped by potential of the altitude of the triangle from the non congruent area. Proving the altitude types 2 congruent acceptable triangles makes use of hypotenuse-leg.