# Prove Line and Angle Theorems

Videos and lessons to help High School students learn how to prove theorems about lines and angles.

Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Common Core: HSG-CO.C.9

Proof-Vertical Angles are Equal
Proving that vertical angles are equal.

Corresponding Angles Converse
If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

Proof: Alternate Interior Angles Are Congruent
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Proof: Alternate Interior Angles Converse
If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

Proof: Consecutive Interior (Same Side) Angles Are Supplementary
If two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary.

Proof: Consecutive Interior Angles Converse
If two lines are cut by a transversal and the consecutive (same side) interior angles are supplementary, then the lines are parallel.

Proof: Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Proof: Perpendicular Bisector Theorem Converse
If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

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