Proofs, Theorems, and Definitions Vocab

Addition Property

if a = b, then a + c = b + c

Subtraction Property

if a = b, then a - c = b - c

Multiplication Property

if a = b, then a * c = b * c

Division Property

if a = b, then a/c = b/c (c ≠ 0)

Substitution Property

if a = b, the a can be replaced by b

Distributive Property

a(b + c) = ab + ac

Reflexive Property

a = a

Symmetric Property

if a = b, then b = a

Transative Property

if a = b and b = c, then a = c

Simplify (CLT)

For any real numbers a, b, c and the variable x

Reflexive Property (≅)

<A ≅ <A and segment AB ≅ segment AB

Symmetric Property (≅)

if <A ≅ <B, then <B ≅ <A

Transitive Property (≅)

if <1 ≅ <2 and <2 ≅ <3, then <1 ≅ <3

The Midpoint Theorem

if M is the midpoint of segment AB, then AM = 1/2(AB); MB = 1/2(AB)

Angle Bisector Theorem

If ray BX is the bisector of <ABC, then m<ABX = 1/2(m<ABC); m<XBC = 1/2(m<ABC)

Vertical Angle Theorem

if two angles are vertical angles, then the angles are congruent

Definition of a Midpoint

if E is the midpoint of segment AF, then segment AE ≅ segment EF

Definition of an Angle Bisector

if ray EB is the bisector of <AEC, then m<AEB = m<BEC

Definition of Supplementary

<AEB + m<BEF = 180 degrees