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Properties of Parallel Lines

Properties of Parallel Lines. Section 3-2. What we will cover…. Corresponding Angles Alternate Interior Angles Same-side Interior Angles What we can prove. Corresponding Angles. Corresponding angles lie in the same place with regard to the original lines and the transversal.

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Properties of Parallel Lines

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  1. Properties of Parallel Lines Section 3-2 section 3-2

  2. What we will cover… • Corresponding Angles • Alternate Interior Angles • Same-side Interior Angles • What we can prove. section 3-2

  3. Corresponding Angles • Corresponding angles lie in the same place with regard to the original lines and the transversal. • If we take an overhead picture of the two intersections, they will lie in the same part of the picture section 3-2

  4. Corresponding Angles on Parallel Lines • When the lines are parallel… • What do you think will be true of the corresponding angles here? • THEY ARE CONGRUENT section 3-2

  5. The Corresponding angles will stay congruent 1 1 2 2 section 3-2

  6. A Proof Given: lines k and l with corresponding angles 1 and 2 Prove: m<2 = m<3 1 k 3 2 l section 3-2

  7. Alternate Interior Angles • Alternate Interior angles lie between the parallel lines and on opposite sides of the transversal. section 3-2

  8. Alternate Interior Angles • When we look at the alternate interior angles on parallel lines… • What do you think about these angles? • THEY ARE CONGRUENT section 3-2

  9. Same-side Interior Angles These will be between the parallel lines on the same side of the transversal • Lets take a look at the same-side interior angles… • Do they look congruent? • NO • They are supplementary. section 3-2

  10. What This Means • When we have parallel lines cut by a transversal: • Corresponding angles are congruent. • Alternate interior angles are congruent. • Same-side interior angles are supplementary section 3-2

  11. Example 1: • What is the value of y if lines a and b are parallel? • What is the relationship between the angles? • Then they must be: (y+50)° a (2y)° b (2y) = (y+50) y = 50 Corresponding Congruent section 3-2

  12. Example 2: • What is the value of x if lines p and q are parallel? • What relationship do the angles have? • This means they are: q (x+20)° (x–10)° p (x+20) + (x–10) = 180 2x + 10 = 180 x = 85 Same-side interior Supplementary section 3-2

  13. What we can prove… • Take a look at these angles… What do you think will be true about these? How about these angles? They are congruent They are congruent **Some texts call these alternate exterior angles. section 3-2

  14. Theorem 3-4 • If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also 1 m<1 = 90˚ section 3-2

  15. Are there parallel lines here? section 3-2

  16. Are these lines parallel? …or even straight? section 3-2

  17. Are these lines parallel? section 3-2

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