3.3 Parallel Lines & Transversals

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Presentation transcript:

3.3 Parallel Lines & Transversals 3.3 Parallel Lines and Transversals 3.3 Parallel Lines & Transversals Define transversal, alternate interior angles, alternate exterior angles, same-side interior angles, and corresponding angles. Make conjectures and prove theorems by using postulates and properties of parallel lines and transversals.

Theorems, Postulates, & Definitions 3.3 Parallel Lines and Transversals Theorems, Postulates, & Definitions Corresponding Angles Postulate : If two lines cut by a transversal are parallel, then corresponding angles are congruent. corresponding angles 2  3

Theorems, Postulates, & Definitions 3.3 Parallel Lines and Transversals Theorems, Postulates, & Definitions Alternate Interior Angles Theorem: If two lines cut by a transversal are parallel, then alternate interior angles are congruent. alternate interior angles 1  3

Theorems, Postulates, & Definitions 3.3 Parallel Lines and Transversals Theorems, Postulates, & Definitions Alternate Exterior Angles Theorem: If two lines cut by a transversal are parallel, then alternate exterior angles are congruent. alternate exterior angles 2  5

Theorems, Postulates, & Definitions 3.3 Parallel Lines and Transversals Theorems, Postulates, & Definitions Same-Side Interior Angles Theorem: If two lines cut by a transversal are parallel, then same-side interior angles are supplementary. same-side interior angles 1 + 4 = 180 GSP Example

Key Skills Identify special pairs of angles. Corresponding angles 3.3 Parallel Lines and Transversals Key Skills Identify special pairs of angles. Corresponding angles 1 and 5 1 and 3 Alternate interior angles Same-side interior angles 1 and 4 Alternate exterior angles 2 and 5

Key Skills Find angle measures formed by parallel lines 3.3 Parallel Lines and Transversals Key Skills Find angle measures formed by parallel lines and transversals. m || n and m1 = 135°. Then m2 = m3 = m5 = 135° and m4 = 45°.

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