Download Geometry Properties, Postulates, and Theorems for Chapter 2

Geometry
Properties, Postulates, and Theorems for Chapter 2
Algebra Properties
Addition Property of Equality
If a = b, then a + c = b + c
Subtraction Property of Equality
If a = b, then a – c = b – c
Multiplication Property of Equality If a = b, then ac = bc
Division Property of Equality
If a = b and c ≠ 0, then
a b
=
c c
(For the above 4 properties, you do the same thing to both sides of the equation.)
Distributive Property
a(b + c) = ab !
+ ac
ab + ac = a(b + c)
Postulates and Theorems
Segment Addition Postulate: If B is between A and C, then AB + BC = AC
Angle Addition Postulate: If S is in the interior of "PQR , then m"PQS + m"SQR = m"PQR
Linear Pair Theorem: If two angles form a linear pair, then they are supplementary (add to 180°).
! angles are supplementary (or
Congruent Supplements (Complements)!Theorem: If two
complementary) to the same angle, then they are congruent.
Right Angle Congruence Theorem: All right angles are congruent.
Vertical Angle Theorem: Vertical angles are congruent.
* Substitution (This is used VERY often!): If a = b and c = b, then a = c.
Here’s an example of how to use substitution:
m"1+ m"2 = 180 o
m"3 + m"4 = 180 o
Using substitution, we can say :
m"1+ m"2 = m"3 + m"4
!