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Understanding Angles in Intersecting Lines and Transversals

Learn to recognize and apply angle relationships in situations involving intersecting, perpendicular, and parallel lines. Understand the angles formed when lines intersect and when parallel lines are crossed by a transversal. Identify types of angles like alternate interior and exterior. Study the theorems related to these angle relationships.

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Understanding Angles in Intersecting Lines and Transversals

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  1. Lesson 4-2 Parallel Lines and Transversals

  2. Ohio Content Standards:

  3. Ohio Content Standards: Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

  4. Ohio Content Standards: Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.

  5. Transversal

  6. Transversal A line that intersects two or more lines, each at different points.

  7. Transversal A line that intersects two or more lines, each at different points. b 1 2 4 3 5 6 c 8 7 r

  8. Transversal A line that intersects two or more lines, each at different points. b 1 2 Interior Angles 4 3 5 6 c 8 7 r

  9. Transversal A line that intersects two or more lines, each at different points. b 1 2 Exterior Angles 4 3 5 6 c 8 7 r

  10. Transversal A line that intersects two or more lines, each at different points. b 1 2 Alternate Interior Angles 4 3 5 6 c 8 7 r

  11. Transversal A line that intersects two or more lines, each at different points. b 1 2 Alternate Exterior Angles 4 3 5 6 c 8 7 r

  12. Transversal A line that intersects two or more lines, each at different points. b 1 2 Consecutive Interior Angles 4 3 5 6 c 8 7 r

  13. Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical.

  14. Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. 1 2 3 4 5 6 7 8

  15. Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. 1 2 3 4 5 6 7 8

  16. Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. 1 2 3 4 5 6 7 8

  17. Theorem 4-1Alternate Interior Angles

  18. Theorem 4-1Alternate Interior Angles If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

  19. Theorem 4-1Alternate Interior Angles If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. 4 3 5 6

  20. Theorem 4-2Consecutive Interior Angles

  21. Theorem 4-2Consecutive Interior Angles If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

  22. Theorem 4-2Consecutive Interior Angles If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. 4 3 5 6

  23. Theorem 4-3Alternate Exterior Angles

  24. Theorem 4-3Alternate Exterior Angles If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.

  25. Theorem 4-3Alternate Exterior Angles If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. 1 2 8 7

  26. p q 7 r 5 1 2 3 6 4 8

  27. t 6 7 B A 8 9 C D

  28. k a 1 (3x+10)° 2 (4x-5)° b

  29. Assignment:Pgs. 152-153 14-38 evens

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