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lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 Warm Up Find the measure of each angle and state the theorem or postulate you used. 1. mÐ1 2. mÐ2 1 2 3. mÐ3 4. mÐ4 5. mÐ5 6. mÐ6 7. mÐ7 4 7 5 6 35o 3 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 33 Proving Lines Parallel GOAL Use the angles formed by a transversal to prove two lines are parallel. Today we are doing the converse of last class! lesson 3.3 Geometry.notebook November 03, 2015 For all theorems/postulates presented last class, what was the hypothesis? then ....angles the conclusion? If 2 lines are parallel lesson 3.3 Geometry.notebook November 03, 2015 33 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. If it is true, it must be stated as a postulate or proved as a separate theorem. Is the converse of a definition true? Share with a partner and use the definition of parallel lines to prove or disprove your point. Parallel lines are coplanar and do not intersect. "If two lines are coplanar and do not intersect, then they are parallel" lesson 3.3 Geometry.notebook November 03, 2015 last class... If two parallel lines are cut by a transversal, then all pairs of corresponding angles are congruent Today... If one pair of corresponding angles are congruent, then the two lines are parallel lesson 3.3 Geometry.notebook November 03, 2015 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 Statements Reasons m∠3 = 4(30) – 80 = 40 Substitute 30 for x. m∠8 = 3(30) – 50 = 40 Substitute 30 for x. m∠3 = m∠8 ∠3 ≅ ∠8 ℓ || m Trans. Prop. of Equality Def. of ≅ ∠s. Conv. of Corr. ∠s Post. lesson 3.3 Geometry.notebook November 03, 2015 Your Turn! #1 Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m∠7 = (4x + 25)°, m∠5 = (5x + 12)°, x = 13 lesson 3.3 Geometry.notebook 33 Proving Lines Parallel More converses from last class... November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. ∠4 ≅ ∠8 lesson 3.3 Geometry.notebook November 03, 2015 33 Proving Lines Parallel Your Turn #2 Name the postulate or theorem that proves p || r. 1. ∠4 ≅ ∠5 2. ∠2 ≅ ∠7 3. ∠3 ≅ ∠7 4. ∠3 and ∠5 are supplementary. lesson 3.3 Geometry.notebook November 03, 2015 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 lesson 3.3 Geometry.notebook November 03, 2015 Your Turn! #3 Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. m∠3 = 2x°, m∠7 = (x + 50)°, x = 50 lesson 3.3 Geometry.notebook November 03, 2015 How we will use this moving forward.... Prove that the quadrilateral is a parallelogram (opposite sides are parallel) 60o 120o 60o 120o lesson 3.3 Geometry.notebook November 03, 2015 Example 4: Proving Lines Parallel m ℓ Given: p || r , ∠1 ≅ ∠3 p 1 2 Prove: ℓ || m r 3 lesson 3.3 Geometry.notebook November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 Proof Pair Work • There are 12 proofs on the paper. Complete 9 of them. • #6, #11 and #12 are bonus proofs (E.C.) • Come to me when you have completed a proof to check your answer. • One of these proofs will be on your chapter test. lesson 3.3 Geometry.notebook Homework: Due Monday 3.3 pg 166 #110, 22, 2435 November 03, 2015 lesson 3.3 Geometry.notebook 33 Proving Lines Parallel Your Turn #3 Given: ∠1 ≅ ∠4, ∠3 and ∠4 are supplementary. Prove: ℓ || m November 03, 2015 lesson 3.3 Geometry.notebook November 03, 2015 Proving Lines are Parallel ~ How could I make sure line p is parallel to line t p t lesson 3.3 Geometry.notebook November 03, 2015