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Lesson 3-3 Objective – To prove lines parallel. Converse of Corresponding Angles Postulate If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Objective – To prove lines parallel. Converse of Corresponding Angles Postulate If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Parallel Line Construction Parallel Line Construction C C B B A A Objective – To prove lines parallel. Converse of Corresponding Angles Postulate If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Objective – To prove lines parallel. Converse of Corresponding Angles Postulate If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Parallel Line Construction Parallel Line Construction D C C B B A A Objective – To prove lines parallel. Converse of Corresponding Angles Postulate If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Parallel Line Construction AC BD B A Given: 2 3 Prove: a b Statement D C Converse of the Alternate Interior Angles Theorem If two coplanar lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. - Construct congruent angles 1) 2 3 2) 1 2 3) 1 3 4) a b 1 3 2 a b Reasons Given Vertical Angles Thm. Transitive Prop of Cong. Conv. of Corres. s Post. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 1 Lesson 3-3 Converse of the Same Side Interior Angles Theorem Converse of If two lines are cut by a transversal Alt. Int. Angles - and the alt. int. angles are congruent Theorem then the lines are parallel. Prove: If 2 & 3 are suppl., then a b. Statement Converse of If two lines are cut by a transversal Alt. Ext. Angles -and the alt. ext. angles are congruent Theorem then the lines are parallel. Converse of If two lines are cut by a transversal SS. Int. Angles - and the SS. int. angles are suppl. Theorem then the lines are parallel. c d a 1 2 3 4 5 6 7 8 1) 2 & 3 are suppl. 2)) 1 & 2 are linear ppair. 3) 1 & 2 are suppl. 4) 1 3 5) a b 9 10 11 12 c 13 14 15 16 b 1 2 a d a 1 2 3 4 5 6 7 8 3 b Reasons Given Def. of linear p pair Linear Pair Theorem Suppl. Thm. Conv. of Corres. s Post. 9 10 11 12 13 14 15 16 b Which lines are proved parallel by the following, why? Which lines are proved parallel by the following, why? 1) 11 15 4) 12 16 c d ,Conv. c d ,Conv. Conv Corres. Corres Conv Corres. Corres s Post. s Post. 2) 5 16 5) 5 13 a b ,Conv. Alt. Ext. a b ,Conv. Corres. s Thm. s Post. 3) 4 9 6) 6 suppl. to 13 a b ,Conv. Alt. Int. a b ,Conv. SS. Int. s Thm. s Thm. 7) 7 3 10) 8 16 c d ,Conv. a b ,Conv. Conv Corres. Corres Conv Corres. Corres s Post. s Post. 11) 10 15 8) 11 14 c d ,Conv. Alt. Int. c d ,Conv. Alt. Ext. s Thm. s Thm. 12) 13 16 9) 4 13 No conclusion No conclusion Prove a b given the following information. 5 6 7 8 1 2 3 4 a 1) m2 m7 2 7 , Def. s a b , Conv. Alt. Int. s Thm. b 2) m1 3x 3 10, 10 m8 5x 5 40, 40 x 25 m1 3(25) 10 85 , Substitution m8 5(25) 40 85 m1 m8 , Substitution 1 8 , Def. s a b , Conv. Alt. Ext. s Thm. Prove a b given the following information. 5 6 7 8 1 2 3 4 a b 3) m1 m7 180 1 4 , Vert. s Thm. m1 m4 , Def. s S b tit ti m4 m7 180 , Substitution m4 & m7 are suppl. , Def. Suppl. s a b , Conv. SS. Int. s Thm. Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014 2