https://file.aiquickdraw.com/mathbot/file/1726649222544hqj6rg5o.jpg

Let's go through each of the problems in the image, focusing on identifying which lines or segments are parallel and justifying the answers.

### Question 7:
This problem shows two pairs of lines intersecting at points labeled B, E, C, and G, with transversal lines intersecting them. The goal is to determine which lines are parallel.

- **Answer**: The lines \( BE \parallel CG \). This is because they are both crossed by the same transversal lines, and corresponding angles are congruent, as indicated by the markings on the diagram.

### Question 8:
Here, a quadrilateral is shown with one diagonal drawn, and the objective is to determine which segments are parallel.

- **Answer**: The lines \( PQ \parallel ST \) are parallel, as indicated by the equal alternate interior angles formed by the transversal diagonal.

### Question 9:
This diagram shows two triangles sharing an angle and two labeled angles that appear to be congruent.

- **Answer**: In this case, there are no directly parallel lines indicated, but the triangles \( \triangle CMA \) and \( \triangle HAR \) might share angle relationships, such as corresponding angles, but this does not indicate parallelism directly.

### Question 10:
A quadrilateral is divided into smaller sections by vertical and horizontal segments.

- **Answer**: The segments \( JM \parallel KL \parallel RS \parallel LM \). These lines are parallel as the corresponding angles formed by transversals are congruent, indicating a parallelogram or rectangle-like shape.

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Do you need further details on any of the explanations or justifications? Here are five related questions to deepen your understanding:

1. What are corresponding angles, and how do they help in proving lines are parallel?
2. Can you explain what alternate interior angles are and how they relate to parallel lines?
3. How do you use transversal lines to determine if two lines are parallel?
4. Why is it important that congruent angles exist when proving lines are parallel?
5. In quadrilaterals, how can you determine if opposite sides are parallel?

**Tip**: Always remember that parallel lines never intersect, and you can prove parallelism by using congruent angles formed by transversals.

Which lines or segments are parallel? Justify your answer based on the given diagrams, involving lines and angles in a series of geometric shapes.

Learn how to identify parallel lines and segments in different geometric shapes using theorems related to corresponding angles and alternate interior angles. This problem focuses on understanding the relationships between lines, angles, and transversals.

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