# Warm Up - PowerPoint PPT Presentation

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Warm Up. Why does this proof reach a false conclusion? a = bGiven a ² = ab Multi. Prop. a ² + a ² = a ² + ab Add. Prop. 2a ² = a ² + ab Simplify 2a ² – 2ab = a ² + ab – 2ab Subt . Prop. 2a ² – 2ab = a ² – ab Simplify

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Warm Up

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### Warm Up

• Why does this proof reach a false conclusion?

a = bGiven

a² = abMulti. Prop.

a² + a² = a² + abAdd. Prop.

2a² = a² + abSimplify

2a² – 2ab = a² + ab – 2abSubt. Prop.

2a² – 2ab = a² – abSimplify

2(a² – ab) = 1(a² – ab)Dist. Prop.

2 = 1Div. Prop.

## Geometry

Segment and Angle Proofs

### Learning Outcomes

• I will be able to write a two-column proof for segment theorems.

• I will be able to write a two-column proof for angle theorems.

### Vocabulary

• A theorem is a true statement that follows as a result of other true statements.

• A two-column proof is a type of proof written as numbered statements and reasons that show the logical order of an argument.

• A paragraph proof is a type of proof written in paragraph form.

• A flow proof is a type of proof that uses arrows to show the flow of logical argument.

### Steps of a proof

• State the Given(s)

• Translate The Given _

• Glean from picture _

• Combine _

• Check for Algebra

• Translate back to prove statement

• Given

• Definition (usually congruence)

• Properties and theorems

• Substitution or transitive property

• Algebraic properties

• Definition (usually congruence)

### Geometry Proofs

• Brainstorm of ways to complete this proof with your partner.

### 1st step: State the given

• State the Given

Given

### 2nd step: Translate Given

• Translate the Given:

Given

FR = ANdefinition of congruence

### 3rd Step: Glean from Picture

• Glean from picture

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN = RNPostulate

### 4th Step: Combine

Combine using transitive property or substitution

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN + RNPostulate

FR + RA = FASubstitution

RA + FR = RN

FA = RNTransitive Property

### 5th Step: Look for algebra

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN + RNPostulate

FR + RA = FASubstitution

RA + FR = RN

FA = RNTransitive Property

### 6th step: Translate to prove statement

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN = RNPostulate

FR + RA = FASubstitution

RA + FR = RN

FA = RNTransitive Property

Definition of Congruence

### Vertical Angle Theorem

• Prove that angles 1 and 3 are congruent or that angles 2 and 4 are congruent.

### Congruent supplements theorem

• If two angles are supplementary to the same angle, then the two angles are congruent.