https://file.aiquickdraw.com/mathbot/file/1728359102324g76rxqih.jpg

The problem shown in the image involves completing a proof to show that two angles, ∠WXY and ∠TUV, are congruent. Here's a breakdown of the statements and reasons presented so far, as well as guidance on how to complete the proof.

### Proof Steps:
1. **Statement:** \( \overrightarrow{TU} \perp \overrightarrow{UV} \)  
   **Reason:** Given
2. **Statement:** \( \overrightarrow{XY} \perp \overrightarrow{WX} \)  
   **Reason:** Given
3. **Statement:** \( m\angle TUV = 90^\circ \)  
   **Reason:** Definition of perpendicular lines
4. **Statement:** \( m\angle WXY = 90^\circ \)  
   **Reason:** Definition of perpendicular lines
5. **Statement:** \( m\angle TUV = m\angle WXY \)  
   **Reason:** Both angles measure 90 degrees
6. **Statement:** \( \angle WXY \cong \angle TUV \)  
   **Reason:** **Definition of congruent angles** (angles with equal measures are congruent)

### The final step needed is adding the reason in line 6:
- **Reason:** **Definition of congruent angles**

This completes the proof, demonstrating that the two angles are congruent because they are both right angles (90°) and therefore have equal measures.

Would you like more details or further explanation on any part of this proof?

Here are 5 related questions to deepen understanding:
1. What does it mean for two lines to be perpendicular?
2. How can you prove that two angles are congruent without knowing their measures?
3. What other types of angle pairs are frequently involved in geometric proofs (e.g., complementary or supplementary)?
4. How does the definition of congruent angles apply to real-world problems?
5. Can perpendicular lines ever form angles that are not right angles?

### Tip:
In geometry proofs, always refer to definitions and theorems that justify each step. This ensures the logical flow and correctness of the proof.

Complete the proof that ∠WXY ≅ ∠TUV.

Learn how to complete a proof showing that ∠WXY is congruent to ∠TUV. This problem involves perpendicular lines and the definition of congruent angles, ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation