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3-1 Properties of Parallel Lines

3-1 Properties of Parallel Lines. L.E.Q. What special angles are created by two lines cut by a transversal and how are they related?. B. A. D. C. Remember:. What would you call two lines which do not intersect?. Parallel.

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3-1 Properties of Parallel Lines

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  1. 3-1 Properties of Parallel Lines L.E.Q. What special angles are created by two lines cut by a transversal and how are they related?

  2. B A D C Remember: What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD

  3. What is a transversal? A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line tis a transversalof lines j, k, and m.

  4. Pairs of Angles Formed By 2 Lines Cut By a Transversal

  5. Alternate interior angles • Two nonadjacent interior angles on opp. Sides of the transversal 3 and 6 4 and 5

  6. Same side interior angles • Two interior angles on the same side of the transversal 4 and 6 3 and 5

  7. Corresponding angles • Two angles in corresponding position relative to the two lines 2 and 6 1 and 5 3 and 7 4 and 8

  8. 0 Which angle is the same side interior angle to D? • A • E • F • H • C B A D C F E G H

  9. 0 Which angle is the alternate interior angle to D? • A • E • F • H • C B A D C F E G H

  10. 0 Which angle is the corresponding angle to C? • A • E • F • H • G B A D C F E G H

  11. Identifying Corresponding Angles • List all the sets of corresponding angles: • 1&5, 2&6, 3&7, 4&8 t 1 2 3 4 5 6 7 8

  12. Identifying Alternate Interior Angles • List all the sets of alternate interior angles: • 3&6, 4&5 t 1 2 3 4 5 6 7 8

  13. Identifying Same-Side Interior Angles • List all the sets of same-side interior angles: • 3&5, 4&6 t 1 2 3 4 5 6 7 8

  14. Corresponding Angles Postulate • If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2

  15. Alternate Interior Angles Theorem • If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4

  16. Same-Side Interior Angles Theorem • If 2 parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. 5 6

  17. Can you determine the measure of specific angles with given information? If angle 1 is 47 degrees find the following: Angle 4 Angle 5 Angle 2 Angle 8

  18. 2x y y - 50 EXAMPLE: Using algebra to find angle measures. • Find the values of x and y. Then find the measures of the angles.

  19. Hw: pg 118-119 #s 1-16 skip 9

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