Help ### Proving Parallel LinesThe image presents a diagram featuring two parallel lines, labeled as $ m $ and $ n $, which are intersected by a transversal line labeled $ t $. The intersections form eight angles, numbered 1 through 8. Each angle is marked at the point where the lines intersect.Here's a detailed transcription of the diagram and the question:---**Diagram Description:**- **Line $ t $:** A transversal line intersecting parallel lines $ m $ and $ n $.- **Line $ m $:** A parallel line intersected by $ t $.- **Line $ n $:** Another parallel line below line $ m $ intersected by $ t $.**Angles formed:**- At the intersection of $ m $ and $ t $: Angles 1, 2, 3, and 4.- At the intersection of $ n $ and $ t $: Angles 5, 6, 7, and 8.---**Question:***What statement could be used to prove that $ m \parallel n $?*1. $ \angle 4 \cong \angle 6 $2. $ m \angle 1 + m \angle 2 = 180^\circ $3. $ m \angle 3 + m \angle 6 = 180^\circ $4. $ \angle 2 \cong \angle 7 $**Options:**- O $ \angle 4 \cong \angle 6 $- O $ m \angle 1 + m \angle 2 = 180^\circ $- O $ m \angle 3 + m \angle 6 = 180^\circ $- O $ \angle 2 \cong \angle 7 $---### Explanation:To determine which statement can be used to prove that lines $ m $ and $ n $ are parallel, let's analyze each option:1. **$ \angle 4 \cong \angle 6 $:** This states that angle 4 is congruent to angle 6. If these angles are corresponding angles, this could help prove the lines are parallel.2. **$ m \angle 1 + m \angle 2 = 180^\circ $:** This states that the sum of the measures of angle 1

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Description: Help ### Proving Parallel LinesThe image presents a diagram featuring two parallel lines, labeled as $ m $ and $ n $, which are intersected by a transversal line labeled $ t $. The intersections form eight angles, numbered 1 through 8. Each ang

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Answered: 8. What statement could be used to…

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8. What statement could be used to prove that m n? O 24살 26 O mz1+m 22= 180° O mZ3 + m = 180° O 22쓸 27 2. 3.

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

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Problem 1CT

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### Proving Parallel Lines

The image presents a diagram featuring two parallel lines, labeled as $ m $ and $ n $, which are intersected by a transversal line labeled $ t $. The intersections form eight angles, numbered 1 through 8. Each angle is marked at the point where the lines intersect.

Here's a detailed transcription of the diagram and the question:

---

**Diagram Description:**

- **Line $ t $:** A transversal line intersecting parallel lines $ m $ and $ n $.
- **Line $ m $:** A parallel line intersected by $ t $.
- **Line $ n $:** Another parallel line below line $ m $ intersected by $ t $.

**Angles formed:**
- At the intersection of $ m $ and $ t $: Angles 1, 2, 3, and 4.
- At the intersection of $ n $ and $ t $: Angles 5, 6, 7, and 8.

---

**Question:**

*What statement could be used to prove that $ m \parallel n $?*

1. $ \angle 4 \cong \angle 6 $
2. $ m \angle 1 + m \angle 2 = 180^\circ $
3. $ m \angle 3 + m \angle 6 = 180^\circ $
4. $ \angle 2 \cong \angle 7 $

**Options:**
- O $ \angle 4 \cong \angle 6 $
- O $ m \angle 1 + m \angle 2 = 180^\circ $
- O $ m \angle 3 + m \angle 6 = 180^\circ $
- O $ \angle 2 \cong \angle 7 $

---

### Explanation:

To determine which statement can be used to prove that lines $ m $ and $ n $ are parallel, let's analyze each option:

1. **$ \angle 4 \cong \angle 6 $:** This states that angle 4 is congruent to angle 6. If these angles are corresponding angles, this could help prove the lines are parallel.

2. **$ m \angle 1 + m \angle 2 = 180^\circ $:** This states that the sum of the measures of angle 1

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