Question

parallel lines and transversals
date________ period
identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Recall Angle Types

• Corresponding: Same position relative to parallel lines and transversal.
• Alternate Interior: Inside parallel lines, opposite sides of transversal.
• Alternate Exterior: Outside parallel lines, opposite sides of transversal.
• Consecutive Interior: Inside parallel lines, same side of transversal.

Step2: Analyze Problem 1

• Two parallel lines, transversal. Angles \( x, y \): same position (above/below, left/right). So corresponding.

Step3: Analyze Problem 2

• Parallel lines, transversal. Angles \( x, y \): outside parallel lines, opposite sides of transversal. So alternate exterior.

Step4: Analyze Problem 3

• Parallel lines, transversal. Angles \( x, y \): inside parallel lines, opposite sides of transversal. So alternate interior.

Step5: Analyze Problem 4

• Parallel lines, transversal. Angles \( x, y \): inside parallel lines, same side of transversal. So consecutive interior.

Step6: Analyze Problem 5

• Parallel lines, transversal (perpendicular? Not needed). Angles \( x, y \): same position. So corresponding.

Step7: Analyze Problem 6

• Parallel lines, transversal. Angles \( x, y \): inside parallel lines, opposite sides? Wait, position: same vertical line? Wait, no—wait, transversal crosses, \( x, y \) are alternate interior? Wait, no, let's recheck. Wait, in problem 6, transversal is vertical? Wait, no, the lines are horizontal, transversal is slanting? Wait, no, the diagram: two horizontal lines, transversal is a line crossing them, \( y \) above, \( x \) below, same side? Wait, no, maybe I misread. Wait, problem 6: transversal is a line, \( y \) and \( x \) are alternate interior? Wait, no, let's use definitions. Wait, problem 6: angles \( x, y \) are inside parallel lines, opposite sides of transversal? No, wait, maybe corresponding? Wait, no, let's do step by step.

Wait, maybe I made a mistake. Let's re-express:

1. Corresponding (same position)
2. Alternate Exterior (outside, opposite sides)
3. Alternate Interior (inside, opposite sides)
4. Consecutive Interior (inside, same side)
5. Corresponding (same position, transversal is vertical, angles at same x - position)
6. Alternate Interior (inside, opposite sides)
7. Corresponding (same position relative to parallel lines and transversal)
8. Corresponding (same position relative to parallel lines and transversal)

(Note: For brevity, each problem's analysis follows the angle type definition. Here, we'll list answers for each sub - problem as per the analysis.)

Answer:

1. Corresponding
2. Alternate Exterior
3. Alternate Interior
4. Consecutive Interior
5. Corresponding
6. Alternate Interior
7. Corresponding
8. Corresponding