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The diagram shows two parallel lines, \( a \) and \( b \), cut by a transversal \( c \), creating several angles labeled 1 through 6. 

The question asks for the theorem that justifies the relationship between certain angles.

### Key angle theorems relevant here:

1. **Same-side interior angles theorem**: The interior angles on the same side of the transversal are supplementary.
2. **Same-side exterior angles theorem**: The exterior angles on the same side of the transversal are supplementary.
3. **Alternate interior angles theorem**: The alternate interior angles (on opposite sides of the transversal) are congruent.
4. **Alternate exterior angles theorem**: The alternate exterior angles (on opposite sides of the transversal) are congruent.

For Part B, depending on the specific angles used in Part A, the correct theorem can vary. If the question in Part A asked about congruent angles on opposite sides of the transversal, then the **Alternate Interior Angles Theorem** or the **Alternate Exterior Angles Theorem** could apply. Otherwise, if it was about angles on the same side, the **Same-Side Interior Angles Theorem** might apply.

Would you like more details about any of these theorems? Let me know if you want to discuss Part A further.

### Relative Questions:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. How do same-side interior angles differ from alternate interior angles?
3. What is the importance of a transversal in angle relationships with parallel lines?
4. Can same-side exterior angles also be supplementary? Why?
5. What geometric concepts would apply if the lines were not parallel?

### Tip:
Always remember that when two parallel lines are cut by a transversal, congruent angles often appear in pairs: alternate interior and exterior angles are equal, and same-side interior angles are supplementary.

Use the diagram to answer the two-part question. Part B: Which theorem will justify your answer in Part A?

Explore the theorems that justify angle relationships formed by parallel lines cut by a transversal. This includes the Same-Side Interior Angles Theorem, Same-Side Exterior Angles Theorem, Alternate Interior Angles Theorem, and Alternate Exterior Angles Theorem. Suitable for students in Grades 8-10.

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