1. Proving Lines Parallel Geometry CP2 (Holt 3-3) K.Santos

2. Parallel Postulate (3-3-2) Through any point P not on line m, there is exactly one line parallel to line m P m

3. Postulates and Theorems To prove two lines are parallel show one pair of… corresponding angles are congruent alternate interior angles are congruent alternate exterior angles are congruent same-side interior angles are supplementary same-side exterior angles are supplementary

4. Example Use the theorems and given information to show that r||s. 1 2 r 3 4 5 6 s 7 8 <4 <8 <4 & <8 are congruent corresponding angles, so the lines are parallel <3 and <5 are supplementary <3 and <5 same side interior angles that are supplementary, so the lines are parallel

5. Example Find the value of x for which m || n. Alternate interior angles would be congruent if lines were parallel. m 14 + 3x n 5x -66 14 + 3x = 5x – 66 3x = 5x -80 -2x = -80 x = 40

6. Example Show lines m and n are parallel. m 3 m<3 = (4x – 80) and m<7 =(3x – 50) and x = 30. n 7 m<3 = 4(30) - 80= 40 m<7 = 3(30) – 50 = 40 This makes sense since these are corresponding angles and they are congruent. So, the lines are parallel.