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# 3.2 theorems about perpendicular lines

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### 3.2 theorems about perpendicular lines

1. 1. Theorems About Perpendicular Lines
2. 2. Comparing Types of Proofs <ul><li>Two-Column Proof </li></ul><ul><li>Paragraph Proof </li></ul><ul><li>Flow Proof </li></ul><ul><ul><li>Uses arrows to show the flow of the logical argument </li></ul></ul>
3. 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. 4. <ul><li>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. </li></ul>2. Paragraph Proof
5. 5. 3. Flow Proof
6. 6. Theorem 3.1 <ul><li>If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. </li></ul>
7. 7. Theorem 3.2 <ul><li>If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. </li></ul>
8. 8. Theorem 3.3 <ul><li>If two lines are perpendicular, then they intersect to form four right angles. </li></ul>
9. 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. 10. Practice and Homework <ul><li>Workbook: Exercise 3.2 </li></ul><ul><li>Textbook: Exercise 3.2 p138: 1-27, odd </li></ul>