**Complete Each Proof** **Exercise 5:**- **Given:** $ m \parallel n, \angle 1 \cong \angle 3 $- **Prove:** $ k \parallel l $| Statements | Reasons ||--------------------------|---------|| $ m \parallel n $ | Given || $ \angle 1 \cong \angle 3 $ | Given |**Explanation of Diagram for Exercise 5:**The diagram shows two parallel lines $ m $ and $ n $ with a transversal intersecting them, creating angles labeled $ 1 $ and $ 3 $. There are also two other lines, $ k $ and $ l $, intersected by the same transversal, showing the relationship that needs to be proven. The given angles imply a pattern that needs to be used to prove the parallelism between lines $ k $ and $ l $.---**Exercise 6:**- **Given:** $ p \parallel q; \angle 1 $ and $ \angle 4 $ are supplementary- **Prove:** $ r \parallel s $(No statements or reasons are filled out for Exercise 6 in the image.)**Explanation of Diagram for Exercise 6:**The diagram displays two parallel lines $ p $ and $ q $ intersected by a transversal, forming angles $ 1 $ and $ 4 $. Additional lines $ r $ and $ s $ intersect the transversal as well, suggesting a relationship between them that has to be proven. In the context of geometry, the concept of supplementary angles often relates to parallel lines, providing a foundational step to proving the unknown parallel lines $ r $ and $ s $.

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Description: **Complete Each Proof** **Exercise 5:**- **Given:** \( m \parallel n, \angle 1 \cong \angle 3 $- **Prove:** $ k \parallel l $| Statements | Reasons ||--------------------------|---------|| $ m \parallel n $ | Given || \( \

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Answered: Compete each proof. 5. Given: m || n;…

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Compete each proof. 5. Given: m || n; Z1 23 Prove: k || 1

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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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

**Complete Each Proof**

**Exercise 5:**

- **Given:** $ m \parallel n, \angle 1 \cong \angle 3 $
- **Prove:** $ k \parallel l $

| Statements | Reasons |
|--------------------------|---------|
| $ m \parallel n $ | Given |
| $ \angle 1 \cong \angle 3 $ | Given |

**Explanation of Diagram for Exercise 5:**

The diagram shows two parallel lines $ m $ and $ n $ with a transversal intersecting them, creating angles labeled $ 1 $ and $ 3 $. There are also two other lines, $ k $ and $ l $, intersected by the same transversal, showing the relationship that needs to be proven. The given angles imply a pattern that needs to be used to prove the parallelism between lines $ k $ and $ l $.

---

**Exercise 6:**

- **Given:** $ p \parallel q; \angle 1 $ and $ \angle 4 $ are supplementary
- **Prove:** $ r \parallel s $

(No statements or reasons are filled out for Exercise 6 in the image.)

**Explanation of Diagram for Exercise 6:**

The diagram displays two parallel lines $ p $ and $ q $ intersected by a transversal, forming angles $ 1 $ and $ 4 $. Additional lines $ r $ and $ s $ intersect the transversal as well, suggesting a relationship between them that has to be proven. In the context of geometry, the concept of supplementary angles often relates to parallel lines, providing a foundational step to proving the unknown parallel lines $ r $ and $ s $.

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