Question

13 classify each angle pair as alternate exterior, alternate interior, same side interior, or corresponding angles: drag & drop the answer

Explanation:

Step1: Analyze First Angle Pair

The first diagram has two parallel lines cut by a transversal. Angles \( x \) and \( y \) are on opposite sides of the transversal and inside the two parallel lines, so they are alternate interior angles. Match with the "Alternate Interior" diagram (middle top).

Step2: Analyze Second Angle Pair

The second diagram: Angles \( x \) and \( y \) are in corresponding positions relative to the parallel lines and transversal (same corner position), so they are corresponding angles. Match with the "Corresponding" diagram (bottom middle).

Step3: Analyze Third Angle Pair

The third diagram: Angles \( x \) and \( y \) are on opposite sides of the transversal and outside the two parallel lines? Wait, no, inside? Wait, no, looking at the lines: two parallel lines, transversal. \( x \) and \( y \) are alternate interior? Wait, no, the third diagram's angle pair: actually, in the third diagram, the angles are alternate exterior? Wait, no, let's recheck. Wait, the third diagram (third row first) has two parallel lines, transversal, angles \( x \) and \( y \) are on opposite sides of transversal, outside? No, inside? Wait, maybe I made a mistake. Wait, the first angle pair (top left) is alternate interior (matches middle top). Second (second row left) is corresponding (matches bottom middle). Third (third row left) is alternate exterior? Wait, no, the alternate exterior diagram (top left of the answer boxes) has angles outside. Wait, the third angle pair: two parallel lines, transversal, angles \( x \) and \( y \) are on opposite sides, outside? No, inside? Wait, maybe the third is alternate exterior? Wait, no, let's recall definitions:

- Alternate Exterior: outside the two lines, opposite sides of transversal.
- Alternate Interior: inside the two lines, opposite sides of transversal.
- Same Side Interior: inside, same side of transversal.
- Corresponding: same position relative to lines and transversal.

First angle pair (top left): inside, opposite sides → Alternate Interior (middle top box).

Second angle pair (second row left): same position (both above the lines, same side of transversal? Wait, no, the second diagram has two transversals? Wait, no, the second diagram: one horizontal transversal and one vertical? No, wait, the second diagram (second row left) has two parallel lines, a slant transversal and a vertical transversal? Wait, no, maybe the second angle pair is corresponding. The corresponding diagram (bottom middle) has angles in same position.

Third angle pair (third row left): two parallel lines, transversal, angles \( x \) and \( y \) are on opposite sides, outside? No, inside? Wait, the third angle pair: the lines are parallel, transversal is slant, angles \( x \) and \( y \) are inside, opposite sides? No, wait, the third angle pair's diagram: the two angles are on opposite sides of transversal, inside the two parallel lines? Wait, no, the third diagram (third row left) has the transversal crossing the two parallel lines, angles \( x \) and \( y \) are alternate interior? Wait, no, maybe the third is alternate exterior. Wait, the alternate exterior diagram (top left answer box) has angles outside. Wait, maybe I messed up. But the key is to match the angle pairs to the correct boxes.

Assuming the first angle pair (top left) matches Alternate Interior (middle top box), second (second row left) matches Corresponding (bottom middle box), third (third row left) matches Alternate Exterior (top left box), and the fourth (bottom left) is a vertical angle or something, but maybe the question is about the first three? Wait, the problem says "classify each angle pair", so let's handle each:

1. Top left angle pair: Alternate Interior → match with Alternate Interior box (middle top).
2. Second row left angle pair: Corresponding → match with Corresponding box (bottom middle).
3. Third row left angle pair: Alternate Exterior → match with Alternate Exterior box (top left).
4. Bottom left: not an angle pair for the given categories (it's a vertical line with 84°, maybe supplementary, but not in the categories).

But since the problem is drag and drop, we need to match each angle pair to the correct box.

Answer:

• Top left angle pair → Alternate Interior (middle top box)
• Second row left angle pair → Corresponding (bottom middle box)
• Third row left angle pair → Alternate Exterior (top left box)

(Note: The specific matching depends on the exact angle positions, but based on definitions, the first is Alternate Interior, second Corresponding, third Alternate Exterior.)