Lesson 3 2 Proof and Perpendicular Lines Goal

Lesson 3. 2 Proof and Perpendicular Lines

Goal 1: Comparing Types of Proofs 2 -Column Proof p Paragraph proof p Flow-chart proof p 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 p Ex 1 p D A B m<ABD = m<DBC and a linear pair, DB AC C 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. p Ex. 2 p F J <FGJ is complementary to <JGH G H

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

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

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

Theorem 3. 3 p If 2 lines are perpendicular, then they intersect to form four right angles. l m

3 Types of Proofs 1. 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. 2. Paragraph Proof This type of proof describes the logical argument with sentences. It is more conversational than a two-column proof. 3. Flow Proof This type of proof uses the same statements and reasons as a twocolumn proof, but the logical FLOW connecting the statements is indicated by arrows.