Proofs & Perpendicular Lines Sec. 3.2 p. 136

GOALS:To learn the characteristics of three different types of proofsTo write a paragraph proofTo learn theorems on perpendicular lines

Theorems 3.1 & 3.2Theorem 3.1

If lines g and h form a linear pair of angles,

then g h

g

h

If 2 sides of adj. acute 's are ,

then the 2 's are complementary.

21

Theorem 3.2

Theorem 3.3

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

l

m

Examples Which theorem or postulate justifies the following

given that the lines are perpendicular?

56

5 6 90m m

2)

1)

l

m3 & 4 are right angles

4

3

Two-Column Proofof Theorem 3.2

Given: BA BC

Prove: 1 & 2 are complementary

Statements Reasons

12

2. is a right angleABC1. Given2. Defn. of lines lines form a right

or

3. 90m ABC 3. Defn. or rt. a right has a measure of 90

or

4. 1 2m m m ABC 4. Angle Addn. Post.

B

A

C

1. BA BC

5. 1 2 90m m 6. 1& 2 are comp.

5. Substitution Prop.6. Defn. of comp. 's

Three types of Proofs & Characteristics

1. Two column proof:• Most formal

• Lists numbered statements in left column and a reason for each statement in the right column

2. Paragraph proof:• Describes the logical argument with sentences

• More conversational

3. Flow proof:• Uses the same statements and reasons as a two-

column proof, but the logical flow connecting the statements is indicated by arrows

See notes sheet for an example of the three types of proofs!