Name the statement: If two sides of a triangle are equal, then the opposite angles are equal.

• A. Theorem
• B. Corollary
• C. Converse of a theorem
• D. Axiom

Answer: (A)

This is a fundamental geometric fact about isosceles triangles. If two sides of a triangle are equal, then the angles opposite those sides are equal. This statement is a theorem because it is a general truth about triangles that can be proven from basic definitions and properties of triangles (such as the angle-sum property and congruence principles). It isn’t a corollary, since it isn’t just a direct, easy consequence of a more basic result but a key result on its own. It isn’t the converse, which would say that if two angles are equal, then the opposite sides are equal. And it isn’t an axiom, since we don’t assume it without proof.