BELL RINGER Lines q, r, and s are distinct in a plane. If line q is perpendicular to line r, and line r is perpendicular to s, then which of following is true? q parallel s q perpendicular to s Q and s are skew Q intersects s S is a transversal of q and r

BELL RINGER cont. Draw a line and label it line q. Draw a line that is perpendicular to line q and label this line r. Draw a line s that is perpendicular to r. What do you see? Remember choices… q parallel s q perpendicular to s Q and s are skew Q intersects s S is a transversal of q and r

Chapter 3 Parallel and Perpendicular Lines Lesson 3.2: Use Parallel Lines and Transversals LEARNING TARGET Solve problems using the corresponding angles postulate, alternate interior angles theorem, alternate exterior angles theorem and consecutive interior angles theorem.

Let’s Investigate! 1 2 3 4 5 6 7 8

Postulate 15 Corresponding Angles If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent. 1 2 3 4 5 6 7 8

Theorem 3.1 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 1 2 3 4 5 6 7 8

Theorem 3.2 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 1 2 3 4 5 6 7 8

Theorem 3.3 Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 1 2 3 4 5 6 7 8

Find angles 1 and 2 for each problem. 1. 2. 120, 120 120, 60 3. 4. 140, 140 135, 45

Let’s Try! Find the value of x. 115o 4 (x + 5)o

Find x. 1. 2. 40 40 3. 4. 110 33

Example 1 – Use properties of parallel lines Find the value of x.

Example 2 – Use properties of parallel lines Find the value of x.

Example 3 – Use properties of parallel lines Find the value of x and y.

Example 4 – Use properties of parallel lines Find the value of x and y.

Homework Page 157 4-18 even, 22,28