LINES CUT BY A TRANSVERSAL

3Geometry Lesson: Proving Lines are Parallel

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

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

9Geometry Lesson: Proving Lines are Parallel Transversals/ angle pairs:

Proving lines parallel Two lines cut by a transversal are parallel if a pair of alternate interior angles are congruent. Theorem : m k Two lines cut by a transversal are parallel if a pair of corresponding angles are congruent. 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. Theorem : l

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

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

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