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Simple Proofs & Theorems 1 and 2 Geometry 1.4 PowerPoint PPT Presentation


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Simple Proofs & Theorems 1 and 2 Geometry 1.4. Definition : Postulates are statements that are assumed true. They are not proved to be true. Definition : Theorems are statements that are proved true using postulates and/or theorems that have already been proved .

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Simple Proofs & Theorems 1 and 2 Geometry 1.4

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Simple proofs theorems 1 and 2 geometry 1 4

Simple Proofs

&

Theorems 1 and 2

Geometry 1.4


Two types of statements postulates theorems

Definition: Postulates are statements that are assumed true. They are not proved to be true.

Definition: Theorems are statements that are proved true using postulates and/or theorems that have already been proved.

Two Types of Statements:Postulates & Theorems


Simple proofs theorems 1 and 2 geometry 1 4

Theorem 1: If two angles are right angles, then they are congruent.

Theorem 2: If two angles are straight angles, then they are congruent.


Simple proofs theorems 1 and 2 geometry 1 4

Theorem 1: If two angles are right angles, then they are congruent.

How to prove a

theorem:

1. Rewrite the “IF – THEN” statement as “Given” and “Prove”

2. Draw a diagram with labels for all referenced objects

3. Write a “Two-Column” Proof


Simple proofs theorems 1 and 2 geometry 1 4

Theorem 2: If two angles are straight angles, then they are congruent.

How to prove a

theorem:

1. Rewrite the “IF – THEN” statement as “Given” and “Prove”

2. Draw a diagram with labels for all referenced objects

3. Write a “Two-Column” Proof


Simple proofs theorems 1 and 2 geometry 1 4

Example of (Very) Simple Two Column Proof:

Given: <A and <B are right angles

Prove:

1.

2.


Simple proofs theorems 1 and 2 geometry 1 4

Example of (Very) Simple Two Column Proof:

Given: m<BAC=30 and m<DAC=30

Prove:

1.

2.


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