Geometry Proofs

Test on 11/13/25-

Transitive Property

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

Substitution Property

If a=b, then (a) may be replaced by (b) an equation

Segment Addition Postulate

If points a, b, and c are on the same line with b between a and c, then ab+bc=ac

Angle Addition Postulate

To find one big angle, you can add the two smaller angles

Vertical Angle theorem

if two angles are vertical angles, then they are congruent

Supplementary Angles

Two angles that equal 180 degrees

Complementary Angles

Two angles that equal 90 degrees

Definition of Right Angles

All right angles are congruent

Definition of linear points/ Linear Pair Theorem

The sum of the measure of a linear pair is 180 degrees- m<1+m<2=180 degrees

Corresponding Angles Theorem

When a transversal intersects two parallel lines, the corresponding angles formed are congruent (equal in measure).

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent (equal in measure)

Alternate Interior Angles Theorem

When two parallel lines are intersected by a transversal, the pairs of alternate interior angles are congruent (equal in measure)

Same Side Interior Angle Theorem

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

Converse of the Corresponding Angle Theorem

If the angles in corresponding positions are equal, the lines must be parallel.  

Converse of the Alternate Interior Angles Theorem

if two lines are intersected by a transversal forming congruent alternate interior angles, then the lines must be parallel.

Converse of the Same Side-Interior Angles Theorem

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

Converse of the Alternate Exterior Angle Theorem