Parallel Lines and Transversals Chapter 3 Section 3.3 Parallel Lines and Transversals

Warm-Up What can you conclude about the angles? Which is not true if m<2=90? The lines are perpendicular. <1 is a right angle. The unlabeled angles are congruent. <1 and <2 are complementary . 1 2

When two parallel lines are cut by a transversal, then … Corresponding angles are  Corresponding Angle Postulate Alternate Interior angles are  Alternate Interior Angle Theorem. Alternate Exterior angles are  Alternate Exterior Angle Theorem Consecutive Interior angles are Supplementary Consecutive Interior Angle Theorem

Perpendicular Transversal Thm. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Find the measure of 1 and 2 Explain your reasoning Corresponding angle Postulate m 2 = 118 Alternate Exterior angle theorem m 1 = 72 Alternate Interior angle theorem m 2 = 180 – 72 = 108 Consecutive Interior angle theorem

Find the measure of 1 and 2 Explain your reasoning Vertical Angle Theorem m 2 = 127 Corresponding angle Postulate

Find the value of x and y and state the reason Vertical Angle Thm y = 81 Corresponding Angle Postulate x = 180 – 98 = 82 Form a linear pair and are supplementary y = 82 Alternate Exterior angle theorem

Find the value of x and y and state the reason Perpendicular Transversal Thm y = 90 If two lines are perpendicular then they form 4 right angles

Find the value of x and state the reason Alt. Int. Angle Thm. 5x – 15 = 80 5x = 95 x = 19 Corresponding Angle Postulate 3(x + 9) = 129 3x + 27 = 129 3x = 102 x = 34

Find the value of x and state the reason Cons. Int. Angle Thm. 4x – 9 + 75 = 180 4x + 66 = 180 4x = 114 x =

Complete the flow proof of the Proof of the Alt. Ext. Angle Thm. a: Given b: Corresponding Angle Postulate c: Vertical Angle Thm d: Transitive