3.4 Parallel Lines and Transversals

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Presentation transcript:

3.4 Parallel Lines and Transversals Goal: Find congruent angles formed when a transversal cuts parallel lines.

Postulate 8 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent. t 1 2 j 3 4 If , then the following are true: 5 6 k 7 8

Find Measures of Corresponding Angles Find the measure of the numbered angle.

Theorem 3.5 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. t 1 2 j 3 4 If , then the following are true: 5 6 k 7 8

Find Measures of Alternate Interior Angles Find the measure of <PQR.

Theorem 3.6 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. t 1 2 j 3 4 If , then the following are true: 5 6 k 7 8

Find Measures of Alternate Exterior Angles Find the measures of <1 and <2. Linear Pair Postulate Substitution Property of = Subtraction Property of =

Theorem 3.7 Same-side Interior Angles Theorem If two parallel lines are cut by a transversal, then same-side interior angles are supplementary. t 1 2 j 3 4 If , then the following are true: 5 6 k 7 8

Find Measures of Same-side Interior Angles Find the measure of the numbered angle.

Use Algebra with Angle Relationships Find the value of x. Corresponding Angles Postulate Subtraction Property of Equality

Homework 3.4 pg. 132 16-42 Even

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