Proving lines are perpendicular

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Proving lines are perpendicular

  1. 1. Proving Lines are Perpendicular
  2. 2. Properties of Perpendicular Lines Perpendicular Lines Postulate: • l1⊥l2 if and only if m1∙m2 = -1 • That is, m2 = -1/m1, The slopes are negative reciprocals of each other. • Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
  3. 3. • In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. Theorem: Perpendicular to Parallel Lines: and Then
  4. 4. • If two coplanar lines are each perpendicular to the same line, then they are parallel to each other. Theorem: Two Perpendiculars:
  5. 5. Proof of Perpendicular to Parallel Lines Theorem Statement Reason 1 l ll m, l ⊥ n Given 2 ∠1 is a right angle Definition of lines⊥ 3 m∠1 = 90o Definition of a right angle 4 m 2∠ = m∠1 Corresponding angles postulate 5 m∠2 = 90o Substitution property of equality 6 ∠2 is a right angle Definition of a right angle 7 m ⊥ n Definition of lines⊥ Given: l ll m and l ⊥ n Prove: m ⊥ n
  6. 6. Examples 1. Line r contains the points (-2,2) and (5,8). Line s contains the points (-8,7) and (-2,0). Is r ⊥ s?
  7. 7. 2. Given the equation of line v is and line w is Is v ⊥ w?
  8. 8. Given the line 3.Find the equation of the line passing through ( 6,1) and perpendicular to the given line. 4. Find the equation of the line passing through ( 6,1) and parallel to the given line.
  9. 9. Homework • Exercise 3.7 page 175: 1-35, odd.
  10. 10. Homework • Exercise 3.7 page 175: 1-35, odd.

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