Mastering Two-Column Proofs: Linear Pair & Alternate Interior Angles

1. Lesson 27 Two-Column Proofs

2. Five Parts of a Two-Column Proof • Given Statement(s): The information that is provided. • Prove Statement: The statement indicating what is to be proved. • Diagram: A sketch that summarizes the provided information. Sometimes you will need to draw a sketch yourself based on given information. • Statement: The specific steps that are written in the left-hand column. • Reasons: Postulates, theorems, definitions, or properties written in the right-hand column, which justify each statement.

3. Prove Thm. 6-3: Linear Pair Thm.GIVEN: ∠SVU is a straight anglePROVE: ∠SVT & ∠TVU are supplementary Statements Reasons Given Def. of Straight Angle Angle Add. Post. Transitive Prop. of Equality Def. of Supplementary Angles • ∠SVU is a straight angle • m∠SVU = 180° • m∠SVU = m∠SVT + m∠TVU • m∠SVT+ m∠TVU = 180° • ∠SVT & ∠TVU are supplementary

4. Prove Thm 10-1: Alt. Int. Angles Thm.GIVEN: a ∥ cPROVE: ∠ 11 ≅ ∠ 14 Statements Reasons Given Corresponding Angles Post. Vert. Angles are Congruent Transitive Prop. of ≅ • a ∥ c • ∠ 10 ≅ ∠ 14 • ∠ 10 ≅ ∠ 11 • ∠ 11 ≅ ∠ 14

5. GIVEN: ∠ 2, ∠ 4, & ∠ 6 are exterior angles of ΔABCPROVE: m∠ 2 + m∠ 4 + m ∠ 6 = 360° statements Reasons Given Exterior Angle Thm. Exterior Angle Thm. Exterior Angle Thm. Addition of Equations Triangle Angle Sum Thm. Substitution Simplify • ∠ 2, ∠ 4, & ∠ 6 are exterior angles of ΔABC • m∠2 = m∠3 +m∠5 • m∠4 = m∠1 + m∠5 • m∠6 = m∠1 + m∠3 • m∠2 + m∠4 + m∠6 = 2(m∠1 + m∠3 + m∠5) • m∠1 + m∠3 + m∠5 = 180° • m∠2 + m∠4 + m∠6 = 2(180°) • m∠2 + m∠4 + m∠6 = 360°

6. Questions? Learning how to write two-column proofs will prepare you for • Lesson 30: Proving Triangles ≅ • Lesson 31: Flowchart & Paragraph Proofs • Lesson 42: Intro. to Coordinate Proofs • Developing a Logical Argument