Geometry: Parallel Lines, Transversals, and Angle Theorems

Alternate Interior Angle Theorem

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

Alternate Exterior Angle Theorem

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Same-Side (Consecutive) Interior Angle Theorem

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Same-Side (Consecutive) Exterior Angle Theorem

If two parallel lines are cut by a transversal, then same-side exterior angles are supplementary.

Vertical Angle Theorem

If two angles are vertical angles, then they are congruent.

Corresponding Angle Postulate

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Linear Pair Postulate

If two angles are a linear pair, then they are supplementary (measures add to 180).

Angle Addition Postulate

The sum of two adjacent angles equals the measure of the entire angle.

Subtraction Property

If a + b = b + c, then a = c.

Transitive Property

If a = b and b = c, then a = c.

Substitution Property

If a = b, then a may be replaced by b in any equation or expression.

Definition of Angle Bisector

A line, segment or ray that splits one angle into two congruent angles.

Definition of Congruence

Angles or segments that have the same (equal) measures.

Definition of Complementary Angles

Two angles that have a sum of 90°.

Definition of Supplementary Angles

Two angles that have a sum of 180°.

Converse of the Alternate Interior Angles Theorem

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

Converse of the Alternate Exterior Angles Theorem

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Converse of the Same-Side (Consecutive) Interior Angles Theorem

If two lines are cut by a transversal so that same-side (consecutive) interior angles are supplementary, then the lines are parallel.

Converse of the Same-Side (Consecutive) Exterior Angles Theorem

If two lines are cut by a transversal so that same-side (consecutive) exterior angles are supplementary, then the lines are parallel.