Question

1. choose the correct answer.

which theorem, term, or corollary is represented by the picture? the bold lines in the pictures represent the hypothesis of the theorem or corollary.
the angles are bold: the sides are not bold.
corollary to the isosceles triangle theorem
cpctc
corollary 2 of the isosceles triangle theorem
converse to the isosceles triangle theorem

Explanation:

The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. The converse of this theorem states that if two angles of a triangle are congruent, then the sides opposite those angles are congruent. In the given picture, the hypothesis (the part we assume) is about the angles (they are bold), and we would be looking at what the conclusion about the sides would be. The Converse to the Isosceles Triangle Theorem fits this as it starts with the angles (hypothesis) to make a claim about the sides (conclusion). CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used when we know triangles are congruent first. The corollaries to the Isosceles Triangle Theorem are more about equilateral/equiangular triangles (e.g., Corollary 1: A triangle is equilateral if and only if it is equiangular; Corollary 2: Each angle of an equilateral triangle measures 60 degrees).

Answer:

Converse to the Isosceles Triangle Theorem