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The image shows a diagram of two intersecting lines forming several angles. Based on the diagram, Sandra concluded that \( \angle 1 \cong \angle 7 \). The question asks which relationship justifies this conclusion.

### Analyzing the Figure:
The figure depicts two parallel lines intersected by a transversal, which forms eight angles. In such cases:
- Angles that are on opposite sides of the transversal but between the two parallel lines are called **alternate interior angles**.
- Alternate interior angles are always congruent.

### Identifying the Angles:
- \( \angle 1 \) and \( \angle 7 \) are on opposite sides of the transversal (the slanted line), but they are **corresponding angles**, not alternate interior angles.

By the **Corresponding Angles Postulate**, if two parallel lines are cut by a transversal, the corresponding angles are congruent. Therefore, \( \angle 1 \cong \angle 7 \) because they are corresponding angles.

### Answer:
The correct relationship is:  
- \( \angle 1 \cong \angle 7 \) because they are corresponding angles.

So the correct answer to the multiple-choice question is:
- \( \angle 1 \cong \angle 7 \) and \( \angle 5 \cong \angle 7 \) (the last option), since this shows both pairs of corresponding angles.

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### Relative Questions:
1. What are corresponding angles and how are they identified?
2. What is the Corresponding Angles Postulate?
3. How do alternate interior angles differ from corresponding angles?
4. What other angle relationships exist in this diagram?
5. Can you prove that two lines are parallel using angle congruencies?

### Tip:
When analyzing angles formed by parallel lines and a transversal, always identify corresponding and alternate interior angles, as they help in solving congruence questions efficiently.

Sandra concluded that \( \angle 1 \cong \angle 7 \). Which relationship correctly justifies Sandra's conclusion?

Learn how to identify and justify congruent angles formed by parallel lines and a transversal. This problem covers key geometric concepts, including corresponding angles and the Corresponding Angles Postulate. Suitable for students in Grades 8-10.

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