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### Geometry

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.

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.

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