https://file.aiquickdraw.com/mathbot/file/1729175102740eujmryja.jpg

Let's go through this proof step-by-step, based on the information given.

### Proof

1. **Statement**: \(\angle 1 \cong \angle 2\), \(\angle 3 \cong \angle 4\)  
   **Reason**: **Given**

2. **Statement**: \(QB \cong QU\)  
   **Reason**: **Given**

3. **Statement**: \(\triangle QTB \cong \triangle QUB\)  
   **Reason**: **ASA Postulate** (Angle-Side-Angle)

4. **Statement**: \(\angle QET \cong \angle QEU\)  
   **Reason**: **CPCTC** (Corresponding Parts of Congruent Triangles are Congruent)

5. **Statement**: \(QE \cong QE\)  
   **Reason**: **Reflexive Property**

6. **Statement**: \(\triangle QET \cong \triangle QEU\)  
   **Reason**: **SAS Postulate** (Side-Angle-Side)

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Would you like more detailed explanations for each step, or do you have any other questions? 

Here are some related questions to expand understanding:

1. What is the ASA postulate, and how is it used in proofs?
2. Can you explain CPCTC and its importance in geometry proofs?
3. How does the reflexive property apply in congruence proofs?
4. How are congruent triangles used to prove properties of other geometric figures?
5. What other postulates or theorems are commonly used in triangle congruence proofs?

**Tip**: In proofs, identifying congruent triangles early helps establish corresponding parts that can be used for further steps.

Complete the proof for triangles QET and QEU, given that angles 1 is congruent to 2, and angles 3 is congruent to 4. Prove that triangle QET is congruent to triangle QEU.

Learn how to prove that triangle QET is congruent to triangle QEU using the ASA postulate and CPCTC. This geometry problem explores key concepts such as congruence and reflexive properties. Suitable for students in Grades 9-10.

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