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3.5 Properties of Parallel Lines Geometry Quiz 3.4 1. m1 90 ; m2 90 1___ 2. 2. If two lines intersect to form a pair of adjacent congruent angles, the lines are _______________. 11) 13) Given; Given; + Prop. of =; + Prop. of =; Transitive Prop. of =; Segment Addition Post. 15) In Class 17) 3. + Post.; 4. Transitive Prop. of =; 5. Substitution 19) 1 and 2 are right 's because lines form right 's. Because 1 and 2 are right 's, m1 m2 90 . 1 2 because m1 m2. 2 5 21) m1 , m2 5 2 9) m1 m2 1 l1 l2 23) Yes 24) No 25) Not enough information. 26) Yes A C O B D 3.5 Properties of Parallel Lines Goal 1: How to identify 's formed by two lines and a transversal. Goal 2: How to use properties of lines. Power Standard #11 Apply skills of conjecture, analysis, and counter-example to formulate a hypothesis and test it. (3.2.1) [2.4-2.6, 3.3-3.6, 4.3, 4.4, 6.4, 8.5] Corresponding Angles Postulate 2 1 If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding Angles Postulate 2 1 If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angles Theorem 2 1 If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Consecutive Interior Angles Theorem 2 1 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 3.5 Properties of Parallel Lines How is 9 related to the other 's? 9 and 10 are a linear pair 4 1 9 and 12 are a linear pair 9 and 11 are vertical 's 3 2 9 and 7 are alternate exterior 's 9 and 3 are alternate exterior 's 9 and 5 are corresponding 's 9 and 1 are corresponding 's 10 11 9 12 8 7 5 6 Alternate Exterior Angles Theorem 2 1 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the second. 3.5 Properties of Parallel Lines Given : l1 l2 Prove: 3 5 Statements Reasons t1 t2 Light enters l1 1. Given 2. t1 t2 2. Given 3. 3 4 3. 4. 4 5 4. 3 5. 3 5 Glass l2 1. l1 l2 5 4 Light exits t2 t1 lines AEA's lines CA's 5. Transitive Prop. 3.5 Properties of Parallel Lines HW 3.5/11-23 odd, 31-33