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Lesson 3.2 Proof and Perpendicular Lines

Lesson 3.2 Proof and Perpendicular Lines. Objectives/Assignment Write different types of proofs Prove results about perpendicular lines Assignment: 2-24 even, 30-36 even. Goal 1: Comparing Types of Proofs. 2-Column Proof Paragraph proof Flow-chart proof Let’s look at page. 136. D. A.

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Lesson 3.2 Proof and Perpendicular Lines

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  1. Lesson 3.2 Proof and Perpendicular Lines Objectives/Assignment Write different types of proofs Prove results about perpendicular lines Assignment: 2-24 even, 30-36 even

  2. Goal 1: Comparing Types of Proofs • 2-Column Proof • Paragraph proof • Flow-chart proof Let’s look at page. 136

  3. D A B C Theorem 3.1 • If two lines intersect to form a linear pair of congruent angles, then the lines are • Ex 1 m<ABD = m<DBC and a linear pair, DB AC Let’s look at page 137 for an example of a Flow Proof

  4. F J G H Theorem 3.2 • If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. • Ex. 2 <FGJ is complementary to <JGH

  5. Examples: Solve for x 1. x 60° ANSWER: 60 + x = 90 -60 -60 x = 30

  6. x 55° Example 2 ANSWER: x + 55 = 90 -55 -55 x = 35

  7. 27° (2x-9)° Example 3 ANSWER: 2x – 9 + 27 = 90 2x +18 = 90 2x = 72 x = 36

  8. l m Theorem 3.3 • If 2 lines are perpendicular, then they intersect to form four right angles.

  9. 3 Types of Proofs 2 Column Proof  The most formal type of proof. It lists numbered statements in the left column and a reason for each statement in the right column. Paragraph Proof  This type of proof describes the logical argument with sentences. It is more conversational than a two-column proof. Flow Proof  This type of proof uses the same statements and reasons as a two-column proof, but the logical FLOW connecting the statements is indicated by arrows.

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