https://file.aiquickdraw.com/mathbot/file/1728255595750ymayl7hg.jpg

ignore 5. fill in the two blanks with the key

The question you provided refers to the Hinge Theorem, which compares angles in two triangles based on the lengths of their sides. The Hinge Theorem (also known as the SAS Inequality Theorem) states that if two sides of one triangle are congruent to two sides of another triangle, but the included angle of one triangle is larger than the included angle of the other triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Given:
- \( AC \cong DE \) and \( BC \cong EF \)
- \( m\angle E > m\angle C \)

According to the Hinge Theorem, since \( m\angle E \) is greater than \( m\angle C \), the third side opposite \( m\angle E \) (which is \( DF \)) must be longer than the third side opposite \( m\angle C \) (which is \( AB \)).

Therefore, the correct answer should be **\( DF > AB \)** (choice c).

Let me know if you want more details or have questions.

---

Here are 5 related questions:
1. What is the Hinge Theorem used for in geometry?
2. Can the Hinge Theorem be applied to non-triangular shapes?
3. How does the Hinge Theorem relate to triangle inequalities?
4. What other geometric theorems help compare angles and sides?
5. How can you prove the Hinge Theorem?

**Tip:** Always check if the sides forming the angles in the triangles are congruent before applying the Hinge Theorem.

AC ≅ DE, BC ≅ EF, m∠E > m∠C. According to the Hinge Theorem, which of the following is true?

This problem applies the Hinge Theorem to compare sides and angles of two triangles. Given AC ≅ DE, BC ≅ EF, and m∠E > m∠C, find the longer side between AB and DF using geometric principles. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation