3-2 Properties of Parallel Lines

2) Postulate 10: Corresponding Angles Postulate If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent. Ex. <1 <5 <2 <6 <3 <7 <4 <8

3) Theorems About Parallel Lines. a) Theorem 3.2 Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Ex. <3 <6 <4 <5

b) Theorem 3.3 Same – side Angles If two parallel lines are cut by a transversal, then the pairs of same - side interior angles are supplementary. Ex. m<4 + m<6 = 180° m<3 + m<5 = 180°

c) Theorem 3.4 Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Ex. < 1 <8 <2 <7

d) Theorem 3.5 Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Ex J K

2) Use the diagram below and find each measure. Also, give the postulate or Theorem. Given: m<1 = 110°

3) If AB ⁄⁄ CD, and AC ⁄⁄ BD, a) Find m<1, m<2, and m<3 b) How many other angles have a measure of 100°?

4) Use properties of parallel lines to find the value of x. 5) Use properties of parallel lines to find the value of x.