Postulates and Theorems

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Presentation transcript:

Postulates and Theorems

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

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

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

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.

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.

Theorems to know We will prove this theorem later today!