### Geometry Problem: Proving Angle Congruence**Given**: - $ r \parallel s, s \parallel t $**Prove**: - $ \angle 6 \cong \angle 7 $**Diagram Explanation**:The diagram on the right shows three parallel lines labeled $ r $, $ s $, and $ t $, intersected by a transversal labeled $ q $. As a result, several angles are formed at the intersections.- Angles are labeled from 1 to 12 around the intersections.- Between $ r $ and $ s $: Angles 2, 3, 8, 9 are formed.- Between $ s $ and $ t $: Angles 4, 5, 10, 11 are formed.### Proof Table| Statements | Reasons ||------------|---------|| | || | || | |**Note**: Fill in the statements and reasons to complete the proof. Use geometric postulates and theorems such as corresponding angles postulate or alternate interior angles theorem to prove angle congruence.

Given, r∥s , s∥tthenr∥s∥t To prove <6 = <7

Answered: Given: r || s, s || t 4. Prove: 17 97…

Math

Geometry

Given: r || s, s || t 4. Prove: 17 97 10 7. 8. 11 12

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Geometry Problem: Proving Angle Congruence

**Given**:
- $ r \parallel s, s \parallel t $

**Prove**:
- $ \angle 6 \cong \angle 7 $

**Diagram Explanation**:
The diagram on the right shows three parallel lines labeled $ r $, $ s $, and $ t $, intersected by a transversal labeled $ q $. As a result, several angles are formed at the intersections.

- Angles are labeled from 1 to 12 around the intersections.
- Between $ r $ and $ s $: Angles 2, 3, 8, 9 are formed.
- Between $ s $ and $ t $: Angles 4, 5, 10, 11 are formed.

### Proof Table

| Statements | Reasons |
|------------|---------|
| | |
| | |
| | |

**Note**: Fill in the statements and reasons to complete the proof. Use geometric postulates and theorems such as corresponding angles postulate or alternate interior angles theorem to prove angle congruence.

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