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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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Warm up
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

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.





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 = AN definition of congruence


3 rd step glean from picture
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
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


5 th step look for algebra
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


6 th step translate to prove statement
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
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.



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