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Exploring Angle Relationships with Parallel Lines and Transversals

Learn to identify and compare angles formed by parallel lines and a transversal through engaging activities. Understand concepts such as corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. Practice measuring and solving for angles using algebraic expressions.

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Exploring Angle Relationships with Parallel Lines and Transversals

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  1. Lesson 3.2 Use Parallel Lines and Transversals Goal: The learner will use angles formed by parallel lines and transversals.

  2. Activity • Draw a pair of parallel lines cut by a transversal. • Trace your drawing on tracing paper. • Move the tracing paper so that 1 is over 5 of the original picture. Are they congruent? • Compare the eight angles and list the congruent pairs. Click on Me for something cool.

  3. Corresponding Angles Postulate • If two parallel lines are cut by a transversal, then corresponding angles are congruent. Identify pairs of corresponding angles. Find the measures of all the angles. 120° 2 5 6 3 4 7 8

  4. Alternate Interior Angles Theorem • If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

  5. Alternate Exterior Angles Theorem • If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

  6. Consecutive Interior Angles Theorem • If two parallel lines are cut by a transversal, then the consecutive angles are supplementary.

  7. Why are the angles congruent? 60 120 115 60 115 60 100 100

  8. Using Algebra and Properties 115 (x + 5)

  9. 92 (2x -4)

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