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Geometry: Properties of Parallel Lines and Transversals

This agenda will discuss the properties of parallel lines and transversals, including alternate interior angle pairs, same-side interior angle pairs, and corresponding angle pairs. Practice assignments and examples are included.

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Geometry: Properties of Parallel Lines and Transversals

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  1. Geometry • Agenda 1. discuss Tests/Spirals 2. 3-1 Properties of Parallel Lines 3. Practice Assignment 4. EXIT

  2. Chapter 3 3-1 Properties of _______Lines

  3. transversal • A line that ________ two coplanar lines at two distinct points. lines a and b are coplanar lines line t is the transversal

  4. Alternate interior angle pairs Interior angles are 3 4 5 and 6. Alternate interior angle pairs are interior angles that are d_________ from each other. Alternate interior angle pairs are ___,___ and ___,___.

  5. Same-side interior angle pairs Interior angles are 3 4 5 and 6. Same-side interior angle pairs are interior angles that are on The ________ _______ of the transversal. Same-side interior angle pairs are ___,___ and ___,___.

  6. Corresponding angle pairs Corresponding angle pairs are one interior angle and one exterior angle that are in the ________ position with respect to each line. Corresponding angle pairs are ___,___ ; ___,___ ; ___,___ and ___,___.

  7. Name angle pairs • Alt. int. s • Same-side int. s • Corres. s

  8. Postulate 3-1Corresponding Angles Postulate • If a transversal intersects two parallel lines, then corresponding angles are ____________.

  9. Theorem 3-1Alternate Interior Angles Theorem • If a transversal intersects two parallel lines, then alternate interior angles are ___________.

  10. Theorem 3-2Same-side Interior Angles Theorem • If a transversal intersects two parallel lines, then same-side interior angles are _________________.

  11. Example #1 • Find the angle measures. m2=35º m6=____ m4=____ m3=____ m8=____

  12. Example #2 • Find the angle measures. m1=____ m2=____ m3=____ m4=____ m5=____ m6=____ m7=____

  13. Example #3 • Find x if m3 = 12x - 8 and m5 = 3x + 10

  14. Example #4 • Determine which lines are parallel if: a. 52 b. 5 supple 6 c. 23 d. 75

  15. Example #5 • Find x and y.

  16. Example #6 • Find x and y.

  17. Example #7 • Given: a||b • Prove: 13 1. a||b 2. 14 3. 43 4. 13

  18. Example #8 • Given: a||b • Prove: 1 supple 2 1. a||b 2. m2+m3=180 3. 31 4. m2+m1=180 5. 1 supple 2

  19. Practice • WB 3-1 #1-16 • EXIT

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