Question

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.
cpctc
isosceles triangle theorem
corollary to the isosceles triangle theorem
corollary 2 of the isosceles triangle theorem

Explanation:

• CPCTC (Corresponding Parts of Congruent Triangles are Congruent): This is about parts of congruent triangles, not directly related to the relationship between angles and sides in a single triangle as shown in the image.
• Isosceles Triangle Theorem: The Isosceles Triangle Theorem states that if two angles of a triangle are congruent (which is what the bold - angled representation might imply as a hypothesis), then the sides opposite those angles are congruent. This matches the general idea of relating angles (hypothesis) to sides (conclusion) in a triangle.
• Corollary to the Isosceles Triangle Theorem: A corollary is a proposition that follows readily from a previous proposition. Since the problem seems to be presenting a basic relationship (angles to sides) rather than a secondary, more specialized result that a corollary would be, this is less likely.
• Corollary 2 of the Isosceles Triangle Theorem: Similar to the above, a corollary 2 would be an even more specialized result, and the image seems to represent the core Isosceles Triangle Theorem relationship.

Answer:

Isosceles Triangle Theorem