Which statement is the Converse of the isosceles triangle theorem?

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Multiple Choice

Which statement is the Converse of the isosceles triangle theorem?

Explanation:
This tests the converse relationship: if two angles in a triangle are equal, then the triangle has two equal sides. When two angles are equal, the sides opposite them must be the same length; otherwise, a longer side would subtend a larger angle, which would contradict the equality of the angles. So the triangle is isosceles because it has two equal sides. The other statements don’t express the converse. One restates the original theorem (equal sides imply equal opposite angles), another states a basic fact about triangles (sum of angles is 180 degrees), and the last describes a parallelogram property.

This tests the converse relationship: if two angles in a triangle are equal, then the triangle has two equal sides. When two angles are equal, the sides opposite them must be the same length; otherwise, a longer side would subtend a larger angle, which would contradict the equality of the angles. So the triangle is isosceles because it has two equal sides.

The other statements don’t express the converse. One restates the original theorem (equal sides imply equal opposite angles), another states a basic fact about triangles (sum of angles is 180 degrees), and the last describes a parallelogram property.

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