1. Postulates and Theorems

2. What is a POSTULATE?
DEFINITION: A statement that is accepted as true without proof.
Like undefined terms; postulates are building blocks of geometry.

3. Postulates to know
Example: If AB = 3x, BC = 2x + 20, and AC = 10x, what is the value of x?
Solution: Since AB + BC = AC then 3x + (2x +20) = 10x
5x + 20 = 10x
20 = 5x
4 = x
x=4

4. Postulates to know
Example: If ∠PQR = 105˚, ∠PQS = 75˚, and ∠SQR = (3x)˚, what is the value of x?

5. Vocabulary terms
Complementary Angles – angles that add up to 90˚ are complementary angles
Supplementary Angles – angles that add up to 180˚ are supplementary angles
Linear Pair – a pair of adjacent [adjacent means “next to”] angles whose non- common sides are opposite rays.

6. What is a THEOREM?
DEFINITION: A statement you can prove is true using a series of logical, deductive, steps.
Proofs of theorems often involve use of postulates and previously proved theorems, as well as deductive reasoning.

7. Theorems to know
We will prove this theorem later today!