Warm Up Why does this proof reach a false

conclusion?

a = b Givena² = ab Multi. Prop.a² + a² = a² + ab Add. Prop.2a² = a² + ab Simplify2a² – 2ab = a² + ab – 2ab Subt. Prop.2a² – 2ab = a² – ab Simplify2(a² – ab) = 1(a² – ab) Dist. Prop.2 = 1 Div. Prop.

GeometrySegment 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.

Paragraph Proof Example

Flow Proof Example

Two-column proof example

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 AdditionRA + AN = RNPostulate

4th Step: CombineCombine using transitive property or substitution

Given FR = AN definition of

congruenceFR + RA = FA Segment AdditionRA + AN + RN PostulateFR + RA = FA SubstitutionRA + FR = RNFA = RN Transitive Property

5th Step: Look for algebra

Given FR = AN definition of congruence

FR + RA = FA Segment AdditionRA + AN + RNPostulateFR + RA = FA SubstitutionRA + FR = RNFA = RN Transitive Property

6th step: Translate to prove statement

Given FR = AN definition of

congruenceFR + RA = FA Segment AdditionRA + AN = RN PostulateFR + RA = FA SubstitutionRA + FR = RNFA = RN Transitive Property Definition of

Congruence

Common Segment Proofs

Common Segment Proofs

Linear pair postulate

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.

Individual practice