The problem requires identifying the relationship between pairs of angles formed by a transversal intersecting parallel lines. The choices are corresponding angles, vertically opposite angles, and alternate angles.

GeometryParallel LinesTransversalsAnglesCorresponding AnglesAlternate Angles
2025/4/29

1. Problem Description

The problem requires identifying the relationship between pairs of angles formed by a transversal intersecting parallel lines. The choices are corresponding angles, vertically opposite angles, and alternate angles.

2. Solution Steps

a) The angles are on the same side of the transversal and in the same relative position (both are above the parallel lines). Therefore, they are corresponding angles.
b) The angles are on opposite sides of the transversal and between the parallel lines. Therefore, they are alternate angles.
c) The angles are on the same side of the transversal. One is an exterior angle and the other is an interior angle. If we extend the transversal line to the second parallel line, we see that the second angle is in the same relative position as the first one. Thus, they are corresponding angles.

3. Final Answer

a) Corresponding angles
b) Alternate angles
c) Corresponding angles

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