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Which segments are parallel?
Which Converse Parallel Property explains why? What Theorem/Statement supports why the lines are parallel? or not?

In the given diagram, we can observe the following parallel segments:

1. **Segments that are parallel:**
   - \( JK \parallel LM \) and \( QR \parallel ST \)
   
   These two sets of segments appear to be part of a parallelogram. A parallelogram has opposite sides that are parallel by definition. Therefore, the segments \( JK \) and \( LM \), as well as \( QR \) and \( ST \), are parallel.

2. **Converse Parallel Property:**
   The **Converse of the Corresponding Angles Postulate** explains why these segments are parallel. The postulate states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

3. **Supporting Theorem:**
   The **Parallelogram Opposite Sides Theorem** (also known as **Theorem 6-3**) supports why these segments are parallel. This theorem states that if a quadrilateral is a parallelogram, then its opposite sides are congruent and parallel.

Would you like more details, or do you have any questions?

Here are 5 related questions for deeper understanding:
1. What is the relationship between the angles at \( K \) and \( L \) in the diagram?
2. How does the Corresponding Angles Postulate apply to parallel lines and transversals in this case?
3. How can we prove that this figure is a parallelogram?
4. What are the properties of parallelograms that apply to this diagram?
5. Can you find other theorems that explain why \( JK \parallel LM \)?

**Tip:** In geometry, recognizing parallel lines often involves checking for congruent angles or applying known properties of quadrilaterals, such as parallelograms.

Which segments are parallel? Which Converse Parallel Property explains why? What Theorem/Statement supports why the lines are parallel? or not?

Discover how to identify parallel segments in a parallelogram diagram. This example explores the Converse of the Corresponding Angles Postulate and the Parallelogram Opposite Sides Theorem, explaining why segments are parallel. Ideal for students in Grades 8-10 studying geometry.

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