Proving lines are parallel

Proving lines are parallel

• 1.
  Proving Lines areParallel
• 2.
  Properties of ParallelLines Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Converse: If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
• 3.
  Biconditional: Two linescut by a transversal are parallel if and only if they the corresponding angles are congruent.
• 4.
  If two parallellines are cut by a transversal, then the pairs of alternate interior angles are congruent. Theorem: Alternate Interior Angles: Converse: If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
• 5.
  If two parallellines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Theorem: Consecutive Interior Angles: Converse: If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
• 6.
  If two parallellines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Theorem: Alternate Exterior Angles: Converse: If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
• 7.
  Proof of AlternateInterior Angles Converse Statement Reason 1 ∠ 1 ≅ ∠ 2 Given 2 ∠ 2 ≅ ∠ 3 Vertical angles theorem 3 ∠ 1 ≅ ∠ 3 Transitive property of congruence 4 l ⊥ m Converse of corresponding angles postulate
• 8.
  Sailing If twoboats sail at an angle of 45 o to the wind and the wind is constant, will their paths ever cross?
• 9.
  Solution Because correspondingangles are congruent, the boats’ paths are parallel. Parallel lines do not intersect, so the boats’ paths will not cross.
• 10.
  Homework Exercise 3.4page 153: 1-37, odd.