Geometric Proofs

Segment Addition Postulate

If point B is between points A and C, then AB+BC=AC

Definition of Congruent Angles

If ∠A ≅ ∠B, then m∠A= m∠B

Definition of Midpoint

If M is the midpoint of AB, then AM ≅ MB

Angle Addition Postulate

If point B is in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC

Definition of Complementary Angles

If ∠A and ∠B are complementary, then
m∠A + m∠B = 90°.

Definition of Supplementary Angles

If ∠A and ∠B are supplementary, then ∠A + m∠ B = 180°.

Vertical Angles Theorem

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

Reflexive Property of Equality

A line segment (or angle) is congruent to itself

Symmetric Property of Equality

m∠A= m∠B, then m ∠B= m ∠A

Transitive Property of Equality

If m ∠B= m ∠A and m ∠B= m ∠C, then m ∠A= m ∠c

Distributive Property of Equality

a(b+c)=ab+ac

Definition of a Right Angle

An angle is a right angle if and only if it equals 90 degrees

Substitution Property

m∠1 + m∠2 = 180°
m∠1 = 68°
68° + m∠2 = 180°