https://file.aiquickdraw.com/mathbot/file/17280035836753xz23oj1.jpg

This proof is aiming to show that \(\angle W \cong \angle V\) based on the given relationships of complementarity. Here's how you can fill in the reasoning column for each statement:

1. **\(\angle U\) and \(\angle W\) are complementary**
   - **Reason**: Given.

2. **\(\angle U\) and \(\angle V\) are complementary**
   - **Reason**: Given.

3. **\(m\angle U + m\angle W = 90^\circ\)**
   - **Reason**: Definition of complementary angles (since complementary angles add up to \(90^\circ\)).

4. **\(m\angle U + m\angle V = 90^\circ\)**
   - **Reason**: Definition of complementary angles.

5. **\(m\angle U + m\angle W = m\angle U + m\angle V\)**
   - **Reason**: Transitive property of equality (since both equal \(90^\circ\)).

6. **\(m\angle W = m\angle V\)**
   - **Reason**: Subtraction property of equality (subtract \(m\angle U\) from both sides).

7. **\(\angle W \cong \angle V\)**
   - **Reason**: Definition of congruent angles (angles with equal measures are congruent).

Let me know if you need more details on the proof or additional clarification!

---

Here are 5 related questions you could explore:
1. What is the definition of supplementary angles?
2. How does the transitive property work in geometric proofs?
3. What are other properties of congruent angles?
4. What are the differences between complementary and supplementary angles?
5. How can you prove two angles are congruent without knowing their specific measurements?

**Tip**: When writing geometric proofs, ensure that every statement has a solid justification to maintain the logical flow.

∠U and ∠W are complementary, and ∠U and ∠V are complementary. Complete the proof that ∠W ≅ ∠V.

Learn how to prove that ∠W is congruent to ∠V through the relationships of complementary angles, using the transitive and subtraction properties of equality. This proof is suitable for students in Grades 8-10 studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation