Warm Up

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# Warm Up - PowerPoint PPT Presentation

Warm Up. Why does this proof reach a false conclusion? a = b Given 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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Presentation Transcript
Warm Up
• Why does this proof reach a false conclusion?

a = b Given

a² = ab Multi. Prop.

a² + a² = a² + ab Add. Prop.

2a² = a² + ab Simplify

2a² – 2ab = a² + ab – 2ab Subt. Prop.

2a² – 2ab = a² – ab Simplify

2(a² – ab) = 1(a² – ab) Dist. Prop.

2 = 1 Div. 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 = AN definition of congruence

3rd Step: Glean from Picture
• Glean from picture

Given

FR = AN definition of congruence

FR + RA = FA Segment Addition

RA + AN = RN Postulate

4th Step: Combine

Combine using transitive property or substitution

Given

FR = AN definition of congruence

FR + RA = FA Segment Addition

RA + AN + RN Postulate

FR + RA = FA Substitution

RA + FR = RN

FA = RN Transitive Property

5th Step: Look for algebra

Given

FR = AN definition of congruence

FR + RA = FA Segment Addition

RA + AN + RN Postulate

FR + RA = FA Substitution

RA + FR = RN

FA = RN Transitive Property

6th step: Translate to prove statement

Given

FR = AN definition of congruence

FR + RA = FA Segment Addition

RA + AN = RN Postulate

FR + RA = FA Substitution

RA + FR = RN

FA = RN Transitive 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.