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Bell Ringer #

Bell Ringer #. 3-1 Properties of Parallel Lines. Transversal: a line that intersects two coplanar lines at two different points. T (transversal). n. 5. 6. 1. 3. m. 4. 2. 7. 8. The angles formed by a transversal have special properties. Alternate interior angles. T. n.

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Bell Ringer #

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  1. Bell Ringer #

  2. 3-1 Properties of Parallel Lines

  3. Transversal: a line that intersects two coplanar lines at two different points. T (transversal) n 5 6 1 3 m 4 2 7 8

  4. The angles formed by a transversal have special properties. Alternate interior angles T n ∠1 and ∠2 are alt. int. angles ∠3 and ∠4 are alt. int. angles 1 3 4 m 2

  5. T n • Same-side interior angles 1 3 ∠1 and ∠4 are same-side int. ∠3 and ∠2 are same-side int. 4 m 2

  6. ∠2 and ∠6 are corresponding ∠1 and ∠7 are corresponding ∠4 and ∠5 are corresponding ∠3 and ∠8 are corresponding T • Corresponding Angles 5 n 6 1 3 4 m 2 7 8

  7. Examples T (transversal) 1. Name a pair of alt. int. angles 2. Name a pair of same-side int. 3. Name 2 pairs of corresponding. 2 1 4 3 n 6 5 8 7 m

  8. Theorems • Corresponding Angles Postulate (3-1) • If a transversal intersects two parallel lines, then corresponding angles are congruent. ∠1 ≅ ∠2

  9. Theorems Alternate Interior Angles Theorem (3-1) • If a transversal intersects two parallel lines, then alternate interior angles are congruent. Same Side Interior Angles Theorem (3-2) • If a transversal intersects two parallel lines, then same-side interior angles are supplementary. ∠1 ≅ ∠3 m∠1 + m∠2 = 180 3 2 1

  10. Two-Column Proof Given: a ‖ b  what you know (either from a picture or statement) Prove: ∠1 ≅ ∠2  what you must show Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4.

  11. Using a two-column proof • Prove theorem 3-2 (If a transversal intersects two parallel lines, then same-side interior angles are supplementary.) • Given: • Prove: ∠1 and ∠2 are supplementary 3 2 1

  12. Find the measures • ∠6 = 50° • Find the measures of the missing angles

  13. Finding angles using algebra • Find the value of x and y 50° x° y° 70°

  14. Finding angles using algebra • Find the values of x and y, then find the measure of the angles. y° 2x° (y-50)°

  15. Practice • Pg 119-120 1-7, 10, 11-16, 17, 23

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