Geometric Proofs

Choices for Reasons in Proofs

Congruent Complements Theorem

If two angles are complementary to the same angle (or to two congruent angles), then the two angles are congruent.

Congruent Supplements Theorem

If two angles are supplementary to the same angle ( or to two congruent angles ), then the two angles are congruent.

Right Angle Theorem

If two angles are right angles, then they are congruent

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary.

Angle Addition Postulate

m<1 + m<2 = m<3

Segment Addition Postulate

AB + BC = AC

Reflexive Property of =

a = a

Symmetric Property of =

If a = b then b = a

Transitive Property of =

If a = b & b = c, then a = c

Distributive

If a( b + c ) then ab + ac

Substitution

If a + b = c & b = 2, then a + 2 = c

Addition Property of =

If a - 4 = 7, then a = 11

Subtraction Property of =

If a + 2 = 10, then a = 8

Multiplication Property of =

If x/2 = 4, then x = 8

Division Property of =

If 3x = 21, then x = 7

Definition of Congruent Angles

Angles that have the same measure

Definition of Congruent Segments

Segments that have the same measure

Definition of Midpoint

Point that divides a segment into two congruent/equal segments

Definition of Segment Bisector

Line, ray or segment that divides a segment into two congruent segments

Definition of Angle Bisector

Ray that divides an angle into two congruent angles

Definition of Right Angle

Angle that measures 90 degrees

Definition of Straight Angle

Angle that measures 180 degrees

Definition of Complementary

Two angles that add up to 90 degrees

Definition of Supplementary

Two angles that add to 180 degrees

Definition of Linear Pair

Adjacent angles that form a straight angle