Intro to Proofs

Addition Property

If a = b and c = d then a + c = b + d

Subtraction Property

If a = b and c = d then a - c = b - d

Multiplication Property

If a = b then a × c = b × c

Division Property

If a = b and c ≠ 0 then a ÷ c = b ÷ c

Substitution Property

If a = b, then anywhere I have a, I can replace it with b (and vice versa)

Reflexive Property (Equality)

a = a, AB = AB, and m∠C = m∠C

Symmetric Property (Equality)

If a = b, then b = a

Transitive Property (Equality)

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

Reflexive Property (Congruence)

Line AB ≅ Line AB, and ∠C ≅ ∠C

Symmetric Property (Congruence)

If Line AB ≅ Line EF, then Line EF ≅ Line AB; If ∠C ≅ ∠H, then ∠H ≅ ∠C

Transitive Property (Congruence)

If Line AB ≅ Line CD and CD ≅ Line EF, then AB ≅ EF

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C

Midpoint Definition

If M is the midpoint of segment AB, then AM ≅ MB
(midpoint → congruent segments)

Midpoint Theorem

If M is the midpoint of segment AB, then AM = 1/2 AB and MB = 1/2 AB

Angle Bisector Definition

If ray BX bisects angle ABC, then ∠1 ≅ ∠2
(angle bisector → congruent angles)

Angle Bisector Theorem

If ray BX bisects angle ABC, then m∠1 = 1/2 m∠ABC and m∠2 = 1/2 m∠ABC