Lesson 3 – 2 Angles and Parallel Lines Geometry Lesson 3 – 2 Angles and Parallel Lines Objective: Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements.

Parallel Lines and Transversals If two lines are parallel and cut by a transversal, then the following is true. Memorize these relationships! Corresponding Angles are congruent. Alternate Interior angles are congruent. Alternate Exterior angles are congruent. Consecutive Interior angles are supplementary.

Postualte 3.1 (Corresponding Angles) If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Theorem 3.1 (Alternate Interior Angles) If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. Theorem 3.2 (Consecutive Interior Angles) If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. Theorem 3.3 (Alternate Exterior Angles)

In the figure. Find the measure of each angle In the figure . Find the measure of each angle. Tell which postulate (or theorems) you used. 72

Explain your reasoning.

30 = 3y + 6 24 = 3y 8 = y Explain your reasoning. Alternate Int.

68 + 3y – 2 = 180 3y + 66 = 180 3y = 114 y = 38 Cons. Int. 4x + 7 = 5x – 13 7 = x – 13 20 = x Alt. Ex.

Theorem 3.4 Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Quiz tomorrow over memorizing angle relationships! Homework Pg. 181 1 – 10 all, 12 – 30 E, 42, 52 – 60 E Quiz tomorrow over memorizing angle relationships!