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Exploring Lines and Angles: Theorem Proofs and Angle Types

Identify and prove theorems about angles formed by parallel lines and a transversal. Explore angle pairs such as corresponding, alternate interior, alternate exterior, and same-side interior angles. Practice calculating angle measures in various scenarios.

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Exploring Lines and Angles: Theorem Proofs and Angle Types

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  1. 2.6 Lines and Angles Warm Up Identify each of the following terms or objects. 1.points that lie in the same plane 2. two angles whose sum is 180° 3.the intersection of two distinct intersecting lines • a pair of adjacent angles whose non-common sides are • opposite rays Coplanar points Supplementary angles A point Linear pair of angles

  2. 2.6 Lines and Angles • Objectives Prove and use theorems about the angles formed by parallel lines and a transversal.

  3. Example 1: • Give an example of each angle pair. • corresponding angles • alternate interior angles • C. alternate exterior angles • D. same-side interior angles

  4. When two parallel lines are cut by a transversal, any pair of angles will either be __________________ or _____________________. supplementary congruent

  5. Example 2: Find mQRS.

  6. Example 3: • Find each angle measure. • mDCE • mECF

  7. Example 4: Find mABD.

  8. Example 5: Find mABD. Finished 1stamd 3rd hour

  9. Example 6: Find the measure of all numbered angles in the diagram. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 35°

  10. Example 7: Proof of the Alternate Exterior Angles Theorem Given: Prove: 2 3 Given Corresp. Post Vert. Thm. Trans. Prop

  11. Example 8: Corresp. Post. Subst. Prop.

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