Properties of Parallel Lines Geometry 3.5

Goal #1: Angles Formed by a Transversal 2 4 3 5 6 7 8 transversal is a line that intersects two or more coplanar lines at different points

Angles formed by a Transversal 1 2 4 3 5 6 7 8 Corresponding 1 and 5 2 and 6 3 and 7 4 and 8 Consecutive Interior 3 and 5 4 and 6 Alternate Interior 3 and 6 4 and 5 Alternate Exterior 1 and 8 2 and 7

Goal #2: Using Properties of Parallel lines 3 4 6 5 8 7 1 What do you think the relationship between the following angles are? m3 m6 m4 m5 m1 m8 m2 m7 m1 m5 m2 m6 m3 m7 m4 m8 m3 and m5 are m4 and m6 are

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1 m1 = m5 m2 = m6 m3 = m7 m4 = m8

Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. l1 l2 t 2 3 4 6 5 8 7 1 m3 + m5 = 180o m4 + m6 = 180o

Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1 m3 = m6 m4 = m5

Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. l1 l2 t 2 3 4 6 5 8 7 1 m1 = m8 m2 = m7

Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the second. t Given: l1 // l2 t  l 1 l1 Therefore, t  l 2 l2

Summary l1 l2 t If l1 // l2 , then, corresponding angles are . 3 4 6 5 8 7 1 If l1 // l2 , then, corresponding angles are . alternate interior angles are . alternate exterior angles are . consecutive interior angles are supplementary.