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This worksheet focuses on identifying different types of angle pairs formed by parallel lines and transversals, such as corresponding angles, alternate interior, alternate exterior, same-side interior, vertical, and adjacent angles. The task also asks to classify whether the angles are **congruent** or **supplementary**.

Let me walk you through the first few problems, based on the markings I can observe, and explain how to determine the types of angles and their relationships:

1. **Problem 1**: 
   - Based on your notes, it seems you identified the angles as **same-side interior** angles, which is correct. These angles are on the same side of the transversal and inside the parallel lines.
   - Since same-side interior angles are supplementary, the sum of angles \(x + y = 180^\circ\).

2. **Problem 2**:
   - You've labeled this as a **linear pair**, which is also correct. A linear pair forms when two angles are adjacent and their non-common sides form a straight line.
   - Linear pairs are **supplementary** because their measures add up to \(180^\circ\).

3. **Problem 3**:
   - You labeled one of the angles as **vertical** and **corresponding**. However, vertical angles are formed when two lines intersect, and these are congruent. In this case, the two angles shown would be **vertical**, and therefore **congruent**.

Let's continue with a few more problems:
4. **Problem 4**: 
   - The angles seem to be **corresponding** angles. Corresponding angles are on the same side of the transversal but one is interior and the other is exterior. They are **congruent**.

5. **Problem 5**:
   - The angles appear to be **alternate interior** angles. These angles lie between the two parallel lines but on opposite sides of the transversal. They are **congruent**.

Would you like more detailed explanations for the remaining problems, or any clarifications?

Here are some relative questions for further exploration:
1. What is the difference between alternate interior and alternate exterior angles?
2. Why are vertical angles always congruent?
3. How do you identify corresponding angles in a transversal diagram?
4. In what situations do angles form a linear pair?
5. Why are same-side interior angles always supplementary when lines are parallel?

**Tip**: When working with angles formed by parallel lines and transversals, remember that congruent angles always have equal measures, while supplementary angles always add up to \(180^\circ\).

Identify each pair of angles as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or adjacent. Then say if they are congruent or supplementary.

Learn to identify angle pairs like corresponding, alternate interior, alternate exterior, same-side interior, vertical, and adjacent angles in a parallel lines and transversals diagram. This worksheet explains whether the angles are congruent or supplementary, focusing on key theorems and properties. Suitable for Grade 8 students.

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