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3.3 Parallel Lines & Transversals

Understand the concepts of transversals and angles when lines are parallel. Learn theorems and postulates to make conjectures and prove properties using corresponding angles, alternate interior angles, and more in Geometry.

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3.3 Parallel Lines & Transversals

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  1. 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.

  2. 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

  3. 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

  4. 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

  5. 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

  6. 3.3 Parallel Lines and Transversals Key Skills Identify special pairs of angles. 1 and 5 Corresponding angles 1 and 3 Alternate interior angles 1 and 4 Same-side interior angles 2 and 5 Alternate exterior angles

  7. 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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