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Warm Up

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- 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

- 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.

- 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.

- 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)

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

- State the Given
Given

- Translate the Given:
Given

FR = ANdefinition of congruence

- Glean from picture
Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN = RNPostulate

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

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN + RNPostulate

FR + RA = FASubstitution

RA + FR = RN

FA = RNTransitive Property

Given

FR = ANdefinition of congruence

FR + RA = FASegment Addition

RA + AN = RNPostulate

FR + RA = FASubstitution

RA + FR = RN

FA = RNTransitive Property

Definition of Congruence

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

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