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
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

4. 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 ≅

5. 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

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