1. Lesson 3.2 Proof and Perpendicular Lines

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

3. 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

4. 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

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

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

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

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

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.