Lesson 31 FLOWCHART & PARAGRAPH PROOFS

Prove Thm. 6-3: Linear Pair Thm. GIVEN: ∠ SVU is a straight angle PROVE: ∠ SVT & ∠ TVU are supplementary STATEMENTS 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 REASONS 1.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 angle PROVE: ∠ 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 angle Given

Prove Thm 10-1: Alt. Int. Angles Thm. GIVEN: a ∥ c PROVE: ∠ 11 ≅ ∠ 14 STATEMENTS 1.a ∥ c 2. ∠ 10 ≅ ∠ ∠ 10 ≅ ∠ ∠ 11 ≅ ∠ 14 REASONS 1.Given 2.Corresponding Angles Post. 3.Vert. Angles are Congruent 4.Transitive Prop. of ≅

GIVEN: a ∥ c PROVE: ∠ 11 ≅ ∠ 14 ∠ 11 ≅ ∠ 14 Transitive Prop. of ≅ ∠ 10 ≅ ∠ 11 Vert. Angles are Congruent ∠ 10 ≅ ∠ 14 Corresponding Angles Post. a ∥ c Given

STATEMENTSREASONS 1.Given 2.Given 3.Def. of Angle Bisector 4.Reflexive of ≅ 5.SAS

ΔMPL ≅ ΔMPN SAS

STATEMENTSREASONS 1.Given 2.Thm 5-4 ( ┴ lines, form ≅ ∠ ’s) 3.Def. of Segment Bisector 4.Reflexive of ≅ 5.SAS

ΔRTQ ≅ ΔSTQ SAS

Conclusion When you are doing proofs, I will give you the option of which format you want to use. 22-Column FFlow Chart P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: LLesson 45: Coordinate Proofs LLesson 48: Indirect Proofs Which means skipping proofs could make these later lessons more challenging