# Isosceles Triangle Conjectures

### Explanation:

An important fact to know is that an isosceles triangle is a triangle in which two of its sides are equal in length. Thus, once you know which two sides are congruent, then the angles opposite them, respectively, are equal in measure.

The converse is similar in explanation. The base angles are the two angles that are equal in measure, and from there, the two sides opposite the angles are congruent.

### The precise statements of the conjectures are:

Conjecture (Isosceles Triangle Conjecture I ): If a triangle is isosceles, then the base angles are congruent.

Converse (Isosceles Triangle Conjecture II ): If two angles in a triangle are congruent, then the triangle is isosceles. In fact, the sides opposite the congruent angles are the congruent sides.

Explanation of the Corollary: If you believe the Isosceles Triangle Conjecture I, then the converse is not so unbelievable. If you are not convinced, then we suggest you try the linked Sketch Pad demonstrations or the further activities provided below.

Question: Can you explain the difference between these two conjectures?

• Key Curriculum Press can provide demo versions of Geometer's Sketch Pad