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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?

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Aim: Do Now:

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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-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.

Geometry Lesson: First Postulates

### 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

“A line segment (or angle) is congruent to itself.”

C

Ex 1:

Ex 2:

B

A

B

D

E

D

A

C

Reflexive Postulate

Reflexive Postulate

### First Postulates – a.k.a. Properties of Equality

Postulate #1 – Reflexive Property of Equality:

“A quantity is equal to itself.” a = a

Geometry Lesson: First Postulates

Ex 1:

Given:

Ex 2:

Given:

A

B

C

D

P

Q

### Postulate #2 - Symmetric Property of Equality:

“An equality may be expressed in either order.”

If a = b,

then, b = a

Symmetric Postulate

Symmetric Postulate

Geometry Lesson: First Postulates

C

B

A

### 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

Given

Given

Transitive Postulate

Def. equilateral triangle

Geometry Lesson: First Postulates

Given:

Prove:

x

y

### Example:

Given

Given

Symmetric Postulate

Transitive Postulate

Def. congruent angles

Geometry Lesson: First Postulates

C

B

A

B

C

D

A

D

S

M

R

L

E

### Examples: First Postulates

1)

2)

Geometry Lesson: First Postulates

A

B

C

D

S

M

R

L

### Ex #1:

Given

Given

Transitive Postulate

Given

Symmetric Postulate

Transitive Postulate

Def. congruent line segments

Geometry Lesson: First Postulates

C

B

A

D

E

### Ex#2

Given

Given

Def. Angle Bisector

Given

Def. Angle Bisector

Transitive Postulate (3,5)

Geometry Lesson: First Postulates