1. What are the first postulates used in geometry proofs? Aim: Do Now:
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.
Geometry Lesson: First Postulates

2. 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.
Arrange proof in 2-column table format. Every statement must have an accompanying reason.
Statements
Reasons
1)Given usually goes first.
1) Given…
2)Conclusions…
2) Definitions, Postulates, Theorems…
3)Conclusions…
3) Definitions, Postulates, Theorems…
4)Prove is last statement
4) Definitions, Postulates, Theorems…
Geometry Lesson: First Postulates

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.
Geometry Lesson: First Postulates

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

5. Postulate #2 - Symmetric Property of Equality:
“An equality may be expressed in either order.”
If a = b,
then, b = a
Ex 1:
Given: A B C D
Ex 2:
Given: P Q
Symmetric Postulate
Symmetric Postulate
Geometry Lesson: First Postulates

6. Postulate #3 – Transitive Property of Equality:
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
Statements
Reasons 1) 2) 3) 4)
Given
Given
Transitive Postulate
Def. equilateral triangle
Geometry Lesson: First Postulates

7. Given: Example: Prove: x y Statements Reasons 1) 2) 3) 4) 5) Given
Symmetric Postulate
Transitive Postulate
Def. congruent angles
Geometry Lesson: First Postulates

8. Examples: First Postulates1) C D S R M L A B 2) C B A E D
Geometry Lesson: First Postulates

9. Ex #1: Given Given Transitive Postulate Given Symmetric PostulateD S R M L A B
Statements
Reasons 1) 2) 3) 4) 5) 6) 7)
Given
Given
Transitive Postulate
Given
Symmetric Postulate
Transitive Postulate
Def. congruent line segments
Geometry Lesson: First Postulates

10. Ex#2 Given Given Def. Angle Bisector Given Def. Angle Bisector
Statements
Reasons 1) 2) 3) 4) 5) 6)
Given
Given
Def. Angle Bisector
Given
Def. Angle Bisector
Transitive Postulate (3,5)
Geometry Lesson: First Postulates