Lesson 27 Two-Column Proofs

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.

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

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

GIVEN: ∠ 2, ∠ 4, & ∠ 6 are exterior angles of ΔABC PROVE: m ∠ 2 + m ∠ 4 + m ∠ 6 = 360° statements Reasons ∠ 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° Given Exterior Angle Thm. Addition of Equations Triangle Angle Sum Thm. Substitution Simplify

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