Isosceles Triangle Proofs

Theorems 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.

Worksheets & Activities on Triangle Proofs

Isosceles Triangle

An 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.

BAC and

BCA are the base angles of the triangle picture on the left. The vertex angle is

ABC

Isosceles Triangle Theorems

The Base Angles Theorem

If 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.

See this isosceles Triangle proof all by itself(opens up new window, making it easier to see entirety of proof below)

Worksheets & Activities on Triangle Proofs

Below is a formula proof that does not use isosceles triangles. However, can you figure out how to rewrite the proof using isosceles triangles and their theorems. (Note: answer to question is forthcoming)

fraction games onlinemathgames.comlaw of sinesambiguous case of the law of sines