When two parallel lines are cut by a
When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? 3. 2 Notes: Angles and Parallel Lines
• In the photo, line t is a transversal of lines a and b, and 1 and 2 are corresponding angles. Since lines a and b are parallel, there is a special relationship between corresponding angle pairs.
Vocab! ***If 2 parallel lines are cut by a transversal, then… Corresponding Angle Postulate - Each pair of corresponding angles is CONGRUENT. List them: Alternate Interior Angles Theorem - Each pair of alternate interior angles is CONGRUENT. List them:
Vocab! ***If 2 parallel lines are cut by a transversal, then… Alternate Exterior - Each pair of alternate exterior angles is CONGRUENT. Angles Theorem List them: Consecutive Interior - Each pair of consecutive interior angles is Angles Theorem SUPPLEMENTARY. List them:
Example 1 •
Example 2 •
You Try! In the figure below , and t is a transversal. If , find the measure of the other angles. m 1 _____ m 2 _____ m 3 _____ m 5 _____ m 6 _____ m 7 _____ m 8 _____
Example 4 •
Vocab! - In a plane, if a line is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other. Perpendicular Transversal Theorem
You Try!
Example 5 Complete the proof. Given: a || b Prove: 4 5 Statements Reasons 1. 2.
Example 6 Complete the proof. Given: a || b Prove: 1 8 Statements Reasons 1. 2.
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