https://file.aiquickdraw.com/mathbot/file/1727374656386jaagtx43.jpg

Let's work through the proof step by step, based on the diagram you uploaded.

We need to prove that line \( \overrightarrow{VX} \perp \overrightarrow{WY} \), meaning that they are perpendicular. Here's the proof:

1. **Step 1: \( \angle WZX \cong \angle VZW \)**
   - **Reason**: These are **vertical angles**, and vertical angles are congruent.

2. **Step 2: \( m\angle VZW + m\angle WZX = 180^\circ \)**
   - **Reason**: These are **supplementary angles**, since they form a linear pair along line \( VX \).

3. **Step 3: \( m\angle VZW + m\angle WZY = 180^\circ \)**
   - **Reason**: **Linear Pair Postulate** or **Definition of a straight angle** (since \( WY \) is a straight line).

4. **Step 4: \( m\angle VZW = 90^\circ \)**
   - **Reason**: Since the sum of the angles is 180° and vertical angles are congruent, it implies that each angle is 90°. This follows from the fact that both angles are equal and add up to 180°.

5. **Step 5: \( \overrightarrow{VX} \perp \overrightarrow{WY} \)**
   - **Reason**: **Definition of perpendicular lines** (lines are perpendicular if they intersect to form a right angle, which has been proven).

Would you like more details or have any further questions about this proof? Here are some additional related questions:

1. How do vertical angles help in geometric proofs?
2. Why are supplementary angles important in proving perpendicularity?
3. What is the Linear Pair Postulate, and how is it used in this proof?
4. How does the definition of perpendicular lines relate to right angles?
5. What are other methods for proving two lines are perpendicular?

**Tip**: Always check for vertical angles and linear pairs in intersecting line diagrams; they often provide crucial relationships in proofs.

Complete the proof that \( \overrightarrow{VX} \perp \overrightarrow{WY} \).

Learn how to prove that \( \overrightarrow{VX} \perp \overrightarrow{WY} \) using geometric properties such as vertical angles and the Linear Pair Postulate. This proof demonstrates step-by-step reasoning to show the relationship between angles and perpendicular lines. 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