Write an equation in slope-intercept form of the line having the given slope and y-intercept: m: –4, b: 3 m: 3, b: –8 m: 3 7 , (0, 1) m: – 2 5 , (0, –6) Problem of the Day

Section 3-5 Proving Lines Parallel

Then Now Objectives You used slopes to identify parallel and perpendicular lines. Recognize angle pairs that occur with parallel lines. Prove the two lines are parallel.

Common Core State Standards Content Standards G.CO.9 – Prove theorems about lines and angles. Mathematical Practices 1) Make sense of problems and persevere in solving them. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Converse of Corresponding Angles Postulate

Proving Lines Parallel

Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. ∠2 ≅ ∠8 ∠3 ≅ ∠11 ∠12 ≅ ∠14 ∠1 ≅ ∠15 m∠8 + ∠13 = 180 ∠8 ≅ ∠6 Example 1

Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. ∠3 ≅ ∠7 ∠9 ≅ ∠11 ∠2 ≅ ∠16 m∠5 + ∠12 = 180 Example 1

Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. ∠CBF ≅ ∠GFH ∠EFB ≅ ∠FBC ∠ACD ≅ ∠KBF m∠BCG + ∠FGC = 180 Example 1

Example 3 Given: ∠5 ≅ ∠15, ∠1 ≅ ∠5 Prove: r ∥ s, ℓ ∥ m Statements Reasons 1. ∠5 ≅ ∠15   2. ∠15 ≅ ∠13 3. ∠5 ≅ ∠13 4. r ∥ s 5. ____________________________ 6. ____________________________ 1. ___________________________________ 2. ___________________________________ 3. ___________________________________ 4. ___________________________________ 5. Given 6. If corr s are ≅, then lines ∥.

p.210 #8 – 15, 48 – 50, 57 Homework