Lesson 3.2 Lesson 3.2 Proof and Proof and

Perpendicular Perpendicular LinesLines

Goal 1: Comparing Types of Goal 1: Comparing Types of ProofsProofs

2-Column Proof Paragraph proof Flow-chart proof

Let’s look at page. 136

Theorem 3.1Theorem 3.1 If two lines intersect to form a linear pair of

congruent angles, then the lines are Ex 1

A B C

Dm<ABD = m<DBC and a linear pair,

DB AC

Let’s look at page 137 for an example of a Flow Proof

Theorem 3.2Theorem 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 xExamples: Solve for x

1.

60°x

ANSWER: 60 + x = 90

-60 -60

x = 30

Example 2Example 2

x55°

ANSWER: x + 55 = 90

-55 -55

x = 35

Example 3Example 3

27°

(2x-9)°

ANSWER: 2x – 9 + 27 = 90

2x +18 = 90

2x = 72

x = 36

Theorem 3.3Theorem 3.3 If 2 lines are perpendicular, then they

intersect to form four right angles.

m

l

3 Types of Proofs 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 two-column proof, but the logical FLOW connecting the statements is indicated by arrows.