Math Problem Statement

If two angles of a triangle are congruent, then the sides opposite those angles are congruent by the converse to the isosceles triangle theorem.

Solution

The statement in the image says:

"If two angles of a triangle are congruent, then the sides opposite those angles are congruent by the converse to the isosceles triangle theorem."

This statement is True. According to the Converse of the Isosceles Triangle Theorem, if two angles in a triangle are congruent (equal), the sides opposite those angles must also be congruent (equal in length). Therefore, the correct answer is:

A. True

Would you like further details or have any questions?

Here are five questions related to the concept:

  1. What is the Isosceles Triangle Theorem?
  2. How does the Converse of the Isosceles Triangle Theorem differ from the original theorem?
  3. Can a triangle with all sides congruent be considered isosceles?
  4. How can the angles of an isosceles triangle help determine the lengths of its sides?
  5. What are the properties of an equilateral triangle in relation to the isosceles triangle?

Tip: When working with triangles, remember that congruent angles often provide information about congruent sides, and vice versa.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Congruence

Formulas

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Theorems

Converse of the Isosceles Triangle Theorem

Suitable Grade Level

Grades 8-10