Warm up
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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

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

Geometry

Segment and Angle Proofs


Learning outcomes

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

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

Paragraph Proof Example


Flow proof example

Flow Proof Example


Two column proof example

Two-column proof example


Steps of a proof

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

Geometry Proofs

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


1 st step state the given

1st step: State the given

  • State the Given

    Given


2 nd step translate given

2nd step: Translate Given

  • Translate the Given:

    Given

    FR = ANdefinition of congruence


3 rd step glean from picture

3rd Step: Glean from Picture

  • Glean from picture

    Given

    FR = ANdefinition of congruence

    FR + RA = FASegment Addition

    RA + AN = RNPostulate


4th step combine

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


5 th step look for algebra

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


6 th step translate to prove statement

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


Common segment proofs

Common Segment Proofs


Common segment proofs1

Common Segment Proofs


Linear pair postulate

Linear pair postulate


Vertical angle theorem

Vertical Angle Theorem

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


Congruent supplements theorem

Congruent supplements theorem

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


Individual practice

Individual practice


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