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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.

 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. $$ \angle $$BAC and $$ \angle $$BCA are the base angles of the triangle picture on the left. The vertex angle is $$ \angle $$ABC

Isosceles Triangle Theorems

The Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Base angles theorem picture for isoscles triangles
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.
 Conver of Base angles theorem picture for isoscles triangles
Proof 1
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Proof 2
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