Lesson 31FLOWCHART & PARAGRAPH PROOFS

Prove Thm. 6-3: Linear Pair Thm.GIVEN: ∠SVU is a straight anglePROVE: ∠SVT & ∠TVU are supplementarySTATEMENTS

1. ∠SVU is a straight angle

2. m SVU = 180°∠3. m SVU = m SVT + m TVU∠ ∠ ∠4. m SVT + m TVU = 180°∠ ∠5. ∠SVT & TVU are supplementary∠

REASONS1. Given

2. Def. of Straight Angle

3. Angle Add. Post.

4. Transitive Prop. of Equality

5. Def. of Supplementary Angles

GIVEN: ∠SVU is a straight anglePROVE: ∠SVT & ∠TVU are supplementary

∠SVT & TVU are ∠supplementary

Def. of Supplementary Angles

m SVT + m TVU = ∠ ∠180°

Transitive Prop. of Equality

m SVU = m SVT + m TVU∠ ∠ ∠Angle Add. Post.

m SVU = 180°∠Def. of Straight Angle

∠SVU is a straight angleGiven

Prove Thm 10-1: Alt. Int. Angles Thm.GIVEN: a ∥ cPROVE: ∠ 11 ≅ ∠ 14STATEMENTS

1. a c∥2. ∠ 10 14≅ ∠3. ∠ 10 11≅ ∠4. ∠ 11 14≅ ∠

REASONS

1. Given2. Corresponding Angles Post.3. Vert. Angles are Congruent4. Transitive Prop. of ≅

GIVEN: a ∥ cPROVE: ∠ 11 ≅ ∠ 14

∠ 11 14≅ ∠Transitive Prop. of

≅

∠ 10 11≅ ∠Vert. Angles are

Congruent

∠ 10 14≅ ∠Corresponding

Angles Post.

a c∥Given

GIVEN: PROVE: ΔMPL ≅ ΔMPN

STATEMENTS

1.

2.

3.

4.

5. ΔMPL ≅ ΔMPN

REASONS

1.Given

2.Given

3.Def. of Angle Bisector

4.Reflexive of ≅5.SAS

GIVEN: PROVE: ΔMPL ≅ ΔMPN

ΔMPL ≅ ΔMPNSAS

Given

Reflexive of ≅

GivenGiven

GIVEN: PROVE: ΔRTQ ≅ ΔSTQ

STATEMENTS

1.

2.

3. ΔRTQ ≅ ΔSTQ

REASONS

1.Given

2.Thm 5-4 ( lines, form ’s)┴ ≅ ∠3.Def. of Segment Bisector

4.Reflexive of ≅5.SAS

GIVEN: PROVE: ΔRTQ ≅ ΔSTQ

ΔRTQ ≅ ΔSTQSAS

Reflexive of ≅

Def. of Segment BisectorGiven

Thm 5-4 Given

Use a Paragraph ProofGIVEN: PROVE: ΔRTQ ≅ ΔSTQ

Since is the perpendicular bisector of , it can be

concluded that is congruent to by theorem 5-4.

The given also means that is congruent to by the

definition of segment bisector. Using the reflexive

property of congruence is congruent . Therefore by

the Side-Angle-Side postulate, ΔRTQ is congruent

to ΔSTQ.

Conclusion When you are doing proofs, I will give you the option of which format you want to use.

2-Column

Flow Chart

Paragraph

I just want you to do the proof. If one format seems easier for you, then use it. Just keep in mind you still must do the same in all styles. A statement must always be backed up by reasoning.

Working with proofs, writing and reading them, will prepare you for:

Lesson 45: Coordinate Proofs

Lesson 48: Indirect Proofs

Which means skipping proofs could make these later lessons more challenging