2. Geometry St. Barnabas H.S. Bronx, NY Geometry Lesson: First Postulates1

3. 2 1) You stand in front of a full-length mirror. How tall is your reflection? 2) John is the same height as Lisa. What conclusion can you make? 3)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.: Lisa is the same height as John. Ans.: Patricia is the same age as Frank. What are the first postulates used in geometry proofs?

4. Geometry Lesson: First Postulates3 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.

5. Geometry Lesson: First Postulates4 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.

6. Geometry Lesson: First Postulates5 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

7. Geometry Lesson: First Postulates6 “An equality may be expressed in either order.” If a = b, then, b = a Ex 1: Given: A B C D Symmetric Postulate Ex 2: Given: PQ Symmetric Postulate Postulate #2 – Symmetric Postulate of Equality:

8. Geometry Lesson: First Postulates7 If quantities are equal to the same quantity, then they are equal to each other. If a = b and b = c, then a = c A B C StatementsReasons 1) 2) 3) 4) Given Transitive Postulate Def. equilateral triangle Postulate #3 – Transitive Postulate of Equality:

9. Geometry Lesson: First Postulates8 Given: Prove: x y StatementsReasons 1) 2) 3) 4) 5) Given Symmetric Postulate Transitive Postulate (Steps 1 & 3) Def. congruent angles

10. Geometry Lesson: First Postulates9 C D S RM L A B C B A E D 1) 2)

11. Geometry Lesson: First Postulates10 StatementsReasons 1) 2) 3) 4) 5) 6) 7) C D S RM L A B Given Transitive Postulate Given Symmetric Postulate Transitive Postulate Def. congruent line segments

12. Geometry Lesson: First Postulates11 C B A E D Given Def. Angle Bisector Given Transitive Postulate (3,5) Def. Angle Bisector StatementsReasons 1) 2) 3) 4) 5) 6)