LINES CUT BY A TRANSVERSAL Geometry Lesson Proving

LINES CUT BY A TRANSVERSAL

Geometry Lesson: Proving Lines are Parallel 3

Aim: When are lines parallel? Do Now: 1) Name 4 pairs of corresponding angles. k 2) Name 2 pairs of alternate interior angles. l 3) Name 2 pairs of alternate exterior angles. 12 34 56 7 8 4) If lines l and k are extended and they never intersect, what can we say about l and k ? l || k 5) If lines l and k are extended and they do intersect, what can we say about l and k ? l is not || k 7

Def. Def: Parallel lines have no points in common or have all points in common. B F D A E C Def: Transversal A transversal is a line that intersects two other lines in two different points. l m k Line m is “transverse” to lines l and k. Geometry Lesson: Proving Lines are Parallel 8

Transversals/ angle pairs: 48 3 7 2 6 1 5 Geometry Lesson: Proving Lines are Parallel 9

Proving lines parallel l 48 3 7 m 2 6 Theorem : 1 5 k Two lines cut by a transversal are parallel if a pair of corresponding angles are congruent. Theorem : Two lines cut by a transversal are parallel if a pair of alternate interior angles are congruent. Theorem : Two lines cut by a transversal are parallel if a pair of interior angles on the same side of the transversal are supplementary. Theorem : Two lines perpendicular to the same line are parallel.

Ex: Proving lines parallel 1) E ( C A D D ( B A 3) A B 48 C C 2) 132 D Or B 4) E C A ( ) D Geometry Lesson: Proving Lines are Parallel B 11

Ex: Proving lines parallel D A C B ? Geometry Lesson: Proving Lines are Parallel 12

C Ex Proving lines parallel: Given: B 12 Prove: 2) 3) D A Statements 1) 3 Reasons 1) Given 2) Given 4) 5) 3) Def. angle bisector 4) 5) Transitive Postulate 6) 6) Geometry Lesson: Proving Lines are Parallel 13