https://file.aiquickdraw.com/mathbot/file/1728578064310pg1kbjp2.jpg

The image contains two questions related to geometry and parallel lines. Let me transcribe and address them:

### Question 1:
**Write a two-column proof. Make sure you write all the statements and reasons.**

Given:  
- \( \triangle A \cong \triangle B \)  
- \( \angle 2 = \angle 3 \)

Prove:  
- \( \angle 1 = \angle 4 \)

There is a diagram provided with angles marked. 

### Question 2:
**Use the diagram to answer the following:**

The diagram shows parallel lines with transversals and angle relationships.

(a) **Find the values of \( x \), \( y \), and \( z \) that make \( p \parallel q \) and \( q \parallel r \). Explain your reasoning.**

The angles shown are:
- \( 30x - 17 \) (an angle on one transversal)
- \( 6y + 87 \) (an angle on the same line)
- \( (4x - 20)^\circ \) (an angle on another transversal)

(b) **Is \( p \parallel r \)? Explain your reasoning.**

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Let me first address the two-column proof (Question 1), then I will proceed to Question 2. Would you like to work through the proof step-by-step, or would you prefer I provide the complete solution?



1. Write a two-column proof. Given: Triangle A congruent to Triangle B and Angle 2 equals Angle 3. Prove: Angle 1 equals Angle 4.
2. Use the diagram to answer: (a) Find the values of x, y, and z that make p parallel to q and q parallel to r. (b) Is p parallel to r?

Solve two-column proof involving congruent triangles and prove angle equality. Additionally, find values of x, y, and z to prove parallel lines using transversal angle relationships. Suitable for students in Grades 8-10.

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