Lesson 3.2 Proof and Perpendicular Lines

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Proofs & Perpendicular Lines Sec. 3.2 p. 136
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Presentation transcript:

Lesson 3.2 Proof and Perpendicular Lines

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

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 A B C D Let’s look at page 137 for an example of a Flow Proof

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

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

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

Example 3 ANSWER: 2x – 9 + 27 = 90 2x +18 = 90 2x = 72 x = 36 27°

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

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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