1. The Addition Postulates and some important definitions, Module 1

2. Postulates to know (and a step-by-step proof)
Given: If AB = 3x, BC = 2x + 20, and AC = 10x, what is the value of x?
AB + BC = AC
Segment Addition Postulate
(3x) + (2x + 20) = (10x)
Substitution
5x + 20 = 10x
Simplification
20 = 5x
Subtraction Property of Equality
4 = x
Division Property of Equality
x = 4
Reflexive Property

3. Given: If ∠PQR = 105˚, ∠PQS = 75˚, and ∠SQR = (3x)˚, what is the value of x?
∠PQS + ∠SQR = ∠PQR
Angle Addition Postulate
75˚ + (3x)˚ = 105˚
Substitution
(3x)˚ = 30˚
Subtraction Property of Equality
x = 30˚
Division Property of Equality

4. Definitions
Congruent – two geometric shapes that are the exact same shape and size
Definition of a midpoint – a point that divides a segment into two congruent segments.
Segment bisector – a line, ray, or other figure that passes through the midpoint of a segment.

5. Definitions
Complementary Angles – two angles whose measures add up to 90˚
Supplementary Angles – two angles whose measures add up to 180˚
Linear Pair – a pair of adjacent angles whose non-common sides are opposite rays.
A Linear Pair of angles are always supplementary!
Angle Bisector – A ray, line, or segment that splits and angle into two congruent angles (in other words – splits an angle in half)

6. Theorems to know