Slopes of Parallel and Perpendicular Lines

Objectives:1. Discover the relationships between the slopes of parallel lines and perpendicular lines.

What type of lines do lines “p” and “q” look like?

parallel lines

Calculate the slope of each.

slope of p = slope of q = = 4

14

1

12

3

What do you notice about the slopes of these two lines?• The slopes are congruent.C-12: Parallel Slope Conj.In a coordinate plane, two lines are _____________if and only if their slopes are ____________.

parallel

congruent

Are these lines parallel?

slope a = -

slope b = -6

1

NO – Slopes are not

5

1

Are these lines parallel?

slope c =

slope d = =5

4

5

410

8

YES – Slopes are

C-22 Perpendicular Slope Conjecture:Two nonvertical lines are _____________ if and only if their slopes are perpendicular

opposite (or negative) reciprocals of each other.

You will be shown the slopes of two lines. On the corner of your notes write down whether each pair of lines are parallel, perpendicular, or neither.

1. slope of line r =

slope of line s =

4

3

4

3

These lines are parallel.

2. slope of line t =

slope of line u =

These lines are perpendicular.

7

4

4

7

3. slope of line t =

slope of line u =

These lines are parallel.

8

6

4

3

4. slope of line t =

slope of line u =

NEITHER!! Slopes are not congruent or opposite

reciprocals of each other.

8

9

9

8

5. slope of line t =

slope of line u = 7

Perpendicular.

7

1