

Isosceles Triangle ProofsTheorems and practice Proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(More about triangle types) Therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.
Isosceles TriangleAn isosceles triangle has two congruent sides and two congruent angles. The congruent angles are called the base angles and the other angle is known as the vertex angle. $$ \angle $$BAC and $$ \angle $$BCA are the base angles of the triangle picture on the left. The vertex angle is $$ \angle $$ABC Isosceles Triangle TheoremsThe Base Angles TheoremIf two sides of a triangle are congruent, then the angles opposite those sides are congruent.Converse of the Base Angles Theorem The converse of the base angles theorem, states that if two angles of a triangle are congruent, then sides opposite those angles are congruent.
Proof 1
Proof 2
Further Reading
Hypotenuse Leg Theorem  Side Side Side  Side Angle Side  Angle Side Angle  Angle Angle Side isosceles triangle proofsCPCTC  indirect proof quiz on all theorems/postulates  Images Free Math Printable Worksheets: Worksheets & Activities on Triangle Proofs 