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3.2 theorems about perpendicular lines
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3.2 theorems about perpendicular lines

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Transcript

  • 1. Theorems About Perpendicular Lines
  • 2. Comparing Types of Proofs
    • Two-Column Proof
    • Paragraph Proof
    • Flow Proof
      • Uses arrows to show the flow of the logical argument
  • 3. Right Angle Congruence Theorem 1. Two Column Proof: All right angles are congruent. Given : 1 and 2 are right angles Prove : 1 ≅ 2 Statement Reason 1 and 2 are right angles Given m 1 = 90 o , m 2 = 90 o Definition of a right angle m 1 = m 2 Transitive property of equality 1 ≅ 2 Definition of congruent angles
  • 4.
    • Because angles 1 and 2 are right angles, their measures are equal to 90 o , by the definition of right angles. Hence by the transitive property of equality, the measure of angle 1 is equal to the measure of angle 2. By the definition of congruent angles, angle 1 is congruent to angle 2.
    2. Paragraph Proof
  • 5. 3. Flow Proof
  • 6. Theorem 3.1
    • If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
  • 7. Theorem 3.2
    • If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
  • 8. Theorem 3.3
    • If two lines are perpendicular, then they intersect to form four right angles.
  • 9. Proof of Theorem 3.2 Prove : 1 + 2 are complementary Statement Reason AB BC Given ABC is a right angle Definition of perpendicular lines m ABC = 90 o Definition of a right angle m 1 + m 2 = m ABC Angle addition postulate m 1 + m 2 = 90 o Substitution property of equality 1 + 2 are complementary Definition of complementary angles
  • 10. Practice and Homework
    • Workbook: Exercise 3.2
    • Textbook: Exercise 3.2 p138: 1-27, odd

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