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6. Contents Lesson 3-1Parallel Lines and Transversals Lesson 3-2Angles and Parallel Lines Lesson 3-3Slopes of Lines Lesson 3-4Equations of Lines Lesson 3-5Proving Lines Parallel Lesson 3-6Perpendiculars and Distance

7. Lesson 2 Contents Example 1Determine Angle Measures OBJECTIVE: To use properties of parallel lines to determine congruent angles (2.9.8E) (M8.C.1.1.3)

8. POSTULATES AND THEOREMS Postulate 3.1 – Corresponding Angles Postulate: If 2 parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Theorem 3.1 – Alternate Interior Angles Theorem: If 2 parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

9. POSTULATES AND THEOREMS Theorem 3.2 – Consecutive Interior Angles Theorem: If 2 parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. Theorem 3.3 – Alternate Exterior Angles Theorem: If 2 parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.

10. POSTULATES AND THEOREMS Theorem 3.4 – Perpendicular Transversal Theorem: In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

11. Answer: Example 2-1a Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution In the figure and Find

12. Example 2-1b Answer: In the figure and Find

13. REVIEW In the figure, m  1 = 93 and m  5 = 75. Find the measure of each angle. 1.  2 2.  3 3.  4 4.  6 5.  7 6.  8 87 93 87 105 75 105

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