The following question was posted on the board as an exit ticket assignment. 

If ∠A≅∠B
 and ​​∠B≅∠C
, which statement and reason can be logically derived from the prior statements? 
A. ∠C≅∠B
 by the symmetric property of congruence.
B. ∠C⋅D≅∠B⋅D
 by the multiplication property of equality.
C.∠C≅∠C
 by the reflexive property of congruence.
D.∠A≅∠C
 by the transitive property of congruence.

Given the problem where:

- ∠A ≅ ∠B (Angle A is congruent to Angle B),
- ∠B ≅ ∠C (Angle B is congruent to Angle C),

We are asked to determine which logical statement can be derived from these two statements.

The **transitive property of congruence** states that if two angles are congruent to the same angle, they are congruent to each other. Specifically, if ∠A ≅ ∠B and ∠B ≅ ∠C, then it logically follows that **∠A ≅ ∠C**.

Thus, the correct statement and reason is:

**D. ∠A ≅ ∠C by the transitive property of congruence.**

Let me know if you'd like more explanation or have any questions! 

Here are 5 related questions to explore:
1. How does the transitive property differ from the symmetric property of congruence?
2. What is the reflexive property of congruence and how is it applied?
3. Can the multiplication property of equality be used with angles, and if so, when?
4. What are some other real-world examples where the transitive property is useful?
5. How do congruence properties relate to the properties of equality in general mathematics?

**Tip:** Always check if relationships between elements (like angles or segments) follow patterns like symmetry, reflexivity, or transitivity when solving geometric problems!

If ∠A ≅ ∠B and ∠B ≅ ∠C, which statement and reason can be logically derived from the prior statements? 
A. ∠C ≅ ∠B by the symmetric property of congruence. 
B. ∠C⋅D ≅ ∠B⋅D by the multiplication property of equality. 
C. ∠C ≅ ∠C by the reflexive property of congruence. 
D. ∠A ≅ ∠C by the transitive property of congruence.

Learn how to apply the transitive property of congruence to solve geometric problems involving angle congruence. This example shows how ∠A ≅ ∠C can be derived from ∠A ≅ ∠B and ∠B ≅ ∠C, demonstrating a key concept in geometry 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