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3-3 Proving Lines Parallel Toolbox Pg. 166 (4-10 even; 16-22 even; 44 why4, 60-61) Holt McDougal Geometry 3-3 Proving Lines Parallel Essential Question HDY use the angles formed by a transversal to prove two lines are parallel? Holt McDougal Geometry 3-3 Proving Lines Parallel Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. Holt McDougal Geometry 3-3 Proving Lines Parallel Holt McDougal Geometry 3-3 Proving Lines Parallel Example 1A: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. ∠4 ≅ ∠8 ∠4 ≅ ∠8 ℓ || m Holt McDougal Geometry ∠4 and ∠8 are corresponding angles. Conv. of Corr. ∠s Post. 3-3 Proving Lines Parallel Example 1B: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m∠ ∠3 = (4x – 80)°, m∠ ∠7 = (3x – 50)°, x = 30 m∠3 = 4(30) – 80 = 40 m∠7 = 3(30) – 50 = 40 m∠3 = m∠7 ∠3 ≅ ∠7 ℓ || m Holt McDougal Geometry Substitute 30 for x. Substitute 30 for x. Trans. Prop. of Equality Def. of ≅ ∠s. Conv. of Corr. ∠s Post. 3-3 Proving Lines Parallel Holt McDougal Geometry 3-3 Proving Lines Parallel Example 2A: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. ∠4 ≅ ∠8 ∠4 ≅ ∠8 ∠4 and ∠8 are alternate exterior angles. r || s Conv. Of Alt. Ext. ∠s Thm. Holt McDougal Geometry 3-3 Proving Lines Parallel Example 2B: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. m∠ ∠2 = (10x + 8)°, m∠ ∠3 = (25x – 3)°, x = 5 m∠2 = 10x + 8 = 10(5) + 8 = 58 Substitute 5 for x. m∠3 = 25x – 3 = 25(5) – 3 = 122 Substitute 5 for x. Holt McDougal Geometry 3-3 Proving Lines Parallel Example 2B Continued Use the given information and the theorems you have learned to show that r || s. m∠ ∠2 = (10x + 8)°, m∠ ∠3 = (25x – 3)°, x = 5 m∠2 + m∠3 = 58° + 122° = 180° ∠2 and ∠3 are same-side interior angles. r || s Holt McDougal Geometry Conv. of Same-Side Int. ∠s Thm. 3-3 Proving Lines Parallel Example 3: Proving Lines Parallel Given: p || r , ∠1 ≅ ∠3 Prove: ℓ || m Holt McDougal Geometry 3-3 Proving Lines Parallel Example 3 Continued Statements Reasons 1. p || r 1. Given 2. ∠3 ≅ ∠2 2. Alt. Ext. ∠s Thm. 3. ∠1 ≅ ∠3 3. Given 4. ∠1 ≅ ∠2 4. Trans. Prop. of ≅ 5. ℓ ||m 5. Conv. of Corr. ∠s Post. Holt McDougal Geometry