Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
The converse of the Isosceles Triangle Theorem states that if a triangle has two congruent angles, then the sides opposite those angles are congruent.
In other words, if we have a triangle such that two angles are congruent, then the sides opposite those angles are also congruent. This is called the converse because it takes the original statement (the Isosceles Triangle Theorem) and reverses the order of the hypothesis and conclusion.
Mathematically, the converse of the Isosceles Triangle Theorem can be expressed as follows:
If angle A = angle B, then side AB = side BA.
It is important to note that the converse may not always be true for all triangles. Even though we know that if a triangle is isosceles, then it has two congruent sides, we cannot always conclude that if a triangle has two congruent sides, it is isosceles. This is why it is important to be careful when using the converse of a theorem in geometric proofs.
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