Math Problem Statement

Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.

A triangle

CPCTC

Corollary 1 to the Isosceles Triangle Theorem

Corollary 2 of the Isosceles Triangle Theorem

Converse to the Isosceles Triangle Theorem

Isosceles Triangle Theorem

Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.

Solution

The image represents Corollary 1 to the Isosceles Triangle Theorem.

In this corollary, it states that if a triangle is isosceles, then the angles opposite the congruent sides are also congruent. In the image, the bold lines indicate the two equal sides of the isosceles triangle, aligning with the hypothesis of this corollary.

Would you like more details on this theorem or how it's applied in geometry? Here are some related questions:

  1. How can we prove the Isosceles Triangle Theorem?
  2. What is the Isosceles Triangle Theorem, and how does it differ from its corollaries?
  3. How does Corollary 2 of the Isosceles Triangle Theorem extend its properties?
  4. What is CPCTC, and how is it used in geometric proofs?
  5. What does the Converse to the Isosceles Triangle Theorem state?

Tip: In geometry, "corollary" often denotes a statement that directly follows from a previously proven theorem, simplifying or extending its application.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties
Isosceles Triangle

Formulas

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Theorems

Isosceles Triangle Theorem
Corollary 1 to the Isosceles Triangle Theorem

Suitable Grade Level

Grades 7-10