Geometry: Angle Theorems

Converse of Corresponding Angles Postulate

If any two lines are crossed by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Converse of Alternate Exterior Angles Theorem

If two coplanar lines are crossed by a transversal so that a pair of alternate exterior angles is supplementary, then the two lines are parallel.

Converse of Alternate Interior Angles Theorem

If two coplanar lines are crossed by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

Converse of Same Side Interior Angles Theorem

If two coplanar lines are crossed by a transversal so that a pair of same-side interior angles is supplementary, then the two lines are parallel.

Alternate Exterior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of alternate exterior angles is congruent.

Alternate Interior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of alternate interior angles is congruent.

Same-side Interior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of same-side interior angles is supplementary.

Corresponding Angles Postulate

If two parallel lines are crossed by a transversal, then the pairs of corresponding angles are always congruent.

Perpendicular Transversal Theorem

In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

Alternate Interior Angles

The pair of angles that are inside the two lines and on opposite sides of the transversal.

Same Side Interior Angles

The pair of angles that are inside the two lines and on the same side of the transversal.

Alternate Exterior Angles

The pair of angles that are outside the parallel lines and on opposite sides of the transversal.