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A midpoint divides a segment into two congruent segments

An angle bisector divides an angle into two congruent parts.

A segment bisector divides a segment at it's midpoint.

Vertical angles are always congruent.

When two parallel lines are cut by a transversal, alternate interior angles are congruent.

A segment or angle is congruent to itself.

This is used when a segment or angle represents the same part in two or more triangles.