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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.
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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
2.6 Lines and Angles • Objectives Prove and use theorems about the angles formed by parallel lines and a transversal.
Example 1: • Give an example of each angle pair. • corresponding angles • alternate interior angles • C. alternate exterior angles • D. same-side interior angles
When two parallel lines are cut by a transversal, any pair of angles will either be __________________ or _____________________. supplementary congruent
Example 2: Find mQRS.
Example 3: • Find each angle measure. • mDCE • mECF
Example 4: Find mABD.
Example 5: Find mABD. Finished 1stamd 3rd hour
Example 6: Find the measure of all numbered angles in the diagram. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 35°
Example 7: Proof of the Alternate Exterior Angles Theorem Given: Prove: 2 3 Given Corresp. Post Vert. Thm. Trans. Prop
Example 8: Corresp. Post. Subst. Prop.