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Transcript
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 3 4 5 6 7 8 2 Postulate 15 Corresponding Angles If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent. 2 6 3 7 1 5 4 8 1 3 4 5 6 7 8 2 Theorem 3.1 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the 1 2 3 4 pairs of alternate interior angles are 5 6 congruent. 4 5 3 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 1 2 are congruent. 3 4 1 8 2 7 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 3 4 3 5 180 4 6 180 5 6 7 8 2 Find angles 1 and 2 for each problem. Let’s Try! Find the value of x. m4 ( x 5) 180 115 ( x 5) 180 x 60 115o 4 (x + 5)o Find x. 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