Direct Proof: Angles, Parallel Lines, and Transversals - Geometric Proofs

Congruence

Having the same measure

Transitive Property

If a = b, and b = c, then a = c *ONLY CONGRUENCY*

Substitution Property of Equality

If a = b, then a may replace b in any equation or expression

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent

Supplementary Angles Axiom (Postulate)

If two angles form a linear pair, then they are supplementary (add up to 180 degrees)

Converse of the Alternate Interior Angle Theorem

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

Converse of the Corresponding Angle Axiom (Postulate)

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

Converse of the Same Side Interior Angle Theorem

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

Same Side Interior Angle Theorem

If two lines are cut by a transversal, the same side interior angles are supplementary

Alternate Exterior Angles Theorem

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

Alternate Interior Angle Theorem

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

Corresponding Angles Axiom (Postulate)

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

Supplementary Angles

TWO angles whose measures have a sum of 180º

Theorem

A conjecture that is proven

Same Side Interior Angles

A pair of angles on one side of a transversal line, and on the inside of the two lines being intersected

Axiom (Postulate)

An accepted statement of fact

Corresponding Angles

Angles at the same location at each intersection

Vertical Angles

Two non - adjacent angles formed by the intersection of the two lines

Alternate Interior Angles

When two lines are crossed by a transversal, the pairs of angles on opposite sides of the transversal, but inside the two lines

Reflexive Property

a = a