2. Aim: Do Now: 1)You stand in front of a full-length mirror. How tall is your reflection? 2)Frank is the same age as Javier. Javier is the same age as Patricia. What conclusion can you make? Ans.: Same height as myself Ans.: Patricia is the same age as Frank. What are the first postulates used in geometry proofs? 3) Solve the linear system for x and y. Ans.: x = 1

3. Postulates and Theorems Postulate: A postulate is a statement that we accept as true without proof. Theorem: A theorem is a statement that can be proved by deductive reasoning.

4. First Postulates Postulate #1 – Reflexive Property of Equality: “A quantity is equal to itself.” a = a AB C D Ex 1: “A line segment (or angle) is congruent to itself.” A B C E D Ex 2: Reflexive Postulate

5. Postulate #2 - Substitution Postulate: “A quantity may be substituted for its equal in any expression.” “ Congruent figures may be substituted for one another” Ex: AB M L K 1 2 3 D C B A E 4 F Given Given:

6. 2-Column Geometry Proofs Given: Information “given” to help start the proof. Prove: The final conclusion that we must make based on the given, postulates, definitions and theorems. StatementsReasons 1)Given usually goes first.1) Given… 2)Conclusions…2) Definitions, Postulates, Theorems… 3)Conclusions…3) Definitions, Postulates, Theorems… 4)Prove is last statement4) Definitions, Postulates, Theorems… Arrange proof in 2-column table format. Every statement must have an accompanying reason.

7. C D S RM L A B C B A E D Examples: First Postulates 1) 2)

8. Ex #1: StatementsReasons 1) 2) 3) 4) 5) 6) C D S RM L A B Given Substitution Postulate Given Substitution Postulate The measure of congruent segments are equal.

9. Ex#2 C B A E D StatementsReasons 1) 2) 3) 4) 5) 6) Given Definition Angle Bisector Given Substitution Postulate (3,5) Definition Angle Bisector

10. You Try One: Given: Prove: B D A C R 4 3 1 2 StatementsReasons 1) 2) 3) 4) 5)