These terms are all related to the study of angles formed when two lines are crossed by a transversal (a third line that intersects them). Here are the definitions:
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Alternate Interior Angles: These are pairs of angles that are on opposite sides of the transversal and inside the two lines. If the two lines are parallel, alternate interior angles are equal.
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Vertical Angles: These are pairs of angles that are opposite each other when two lines intersect. Vertical angles are always congruent (equal in measure).
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Corresponding Angles: These angles are on the same side of the transversal and in corresponding positions relative to the two lines. If the lines are parallel, corresponding angles are equal.
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Alternate Exterior Angles: These are pairs of angles that are on opposite sides of the transversal and outside the two lines. Like alternate interior angles, if the two lines are parallel, alternate exterior angles are equal.
These concepts are fundamental in geometry, especially when dealing with parallel lines and transversals.