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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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Presentation Transcript
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.