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.
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?