https://file.aiquickdraw.com/mathbot/file/1726236710074gaj8tl6t.jpg

To solve this geometry problem, let's analyze the given information and use it to prove the desired statement.

### **Given:**
1. \( VW \cong YX \) (Side congruence)
2. \( ZW \cong ZX \) (Side congruence)

### **To Prove:**
\( VZ \cong YZ \)

### **Proof:**
We can use the **Side-Side-Side (SSS) Congruence Theorem** or **Isosceles Triangle Theorem** to prove this statement.

1. From the diagram, triangles \( VWZ \) and \( XYZ \) are present.
2. According to the given information:
   - \( VW \cong YX \)
   - \( ZW \cong ZX \)
   - Both triangles share the side \( VZ \) and \( YZ \).
3. Since \( ZW \) and \( ZX \) are congruent and share a common vertex \( Z \), both triangles can be considered isosceles with \( VZ \) and \( YZ \) acting as corresponding sides.
4. By the isosceles property, \( VZ \) is congruent to \( YZ \), as the corresponding sides of the triangles.

### **Conclusion:**
Therefore, \( VZ \cong YZ \), completing the proof.

Would you like more details or have any questions?

### **Related Questions:**
1. How do you prove congruence using other properties like Angle-Side-Angle (ASA)?
2. What other theorems can be used for triangle congruence?
3. How would the proof change if the sides were not congruent but angles were?
4. What is the significance of the shared vertex in this proof?
5. Can this proof be extended to non-isosceles triangles?

**Tip:** When proving congruence, always identify corresponding sides and angles to find the easiest pathway using congruence theorems.

Given that VW is congruent to YX and ZW is congruent to ZX, prove that VZ is congruent to YZ.

Learn how to prove that VZ is congruent to YZ using the Side-Side-Side (SSS) Congruence Theorem and the Isosceles Triangle Theorem. This problem covers key geometric concepts and is 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