Proving Lines Parallel

Slope of Lines

Slope: the rise and run of a line

To find slope, you use the following formula… y2 − y1𝑚 = x2 – x1

Ex. Find the slope between the given points.(-3, 5) and (6, -2)

−2 −5 −7=m = 6 −−3 9

Types of Slope

1. Positive SlopeA positive number.

2. Negative Slope

A negative number.

3. No Slope 4. Zero SlopeZero divided by a number.

A number divided by zero.

You try…

Find the slope between to given points.2.1. (2, -3) (-2, 8) (-8, -1) (-4, -3)

3. (8, -4) (0, 7) 4. (-5, 1) (-2, -2)

You try…

Find the slope between to given points.2.1. (2, -3) (-2, 8) (-8, -1) (-4, -3)

3. (8, -4) (0, 7) 4. (-5, 1) (-2, -2)

Find the slope of the parallel lines.(-4, 2) (-1, 3) 3 − 2 1𝑚 = =−1 − −4 3

(-1, 3)

(-4, 2)

(1, -5) (4, -4)−4 − −5 1𝑚 = =4 − 1 3(4, -4)

(1, -5)

So, the slope of parallel lines are always the SAME!!!

Find the slope of the perpendicular lines.

(-5, -2) (-3, 1) 1 − −2 3𝑚 = =−3 − −5 2(-3, 1) (3, -4) (0, -2)−2 − −4 2 −2𝑚 = = =0 − 3 −3 3(0, -2)

(-5, -2)

(3, -4)

So, the slope of perpendicular lines are always OPPOSITE,RECIPORCALS!!!

Determine whether line AB and line CD areparallel, perpendicular or neither.

1. A (-2, -5) B(4, 7) C(0, 2) D(8, -2) 2. A (-8, -7) B(4, -4) C(-2,-5) D(1, 7)

7−− 5 = 12 −4 −−7 = 3

1AB = = 2 AB = =4−−2 6 4−−8 12 4 − 2−2 = −4 1 7 −−5 12 CD = = − CD = = = 48−0 8 2 1−−2 3

Since the slopes

reciprocals, then

be PARALLEL.

are opposite,the lines would

Although the slopes are reciprocals,

they are not opposites, so these

lines would be NEITHER.

You try…

Determine whether line AB and line CDneither.

are parallel, perpendicular or

1. A(-3, -2), B(9, 1), C(3, 6), D(5, -2)

2. A(-4, 0), B(0, 3), C(-4, -3), D(8, 6)

3. A(-10, 7), B(2, 1), C(4, 0), D(6, 1)

You try…

Determine whether line AB and line CDneither.

are parallel, perpendicular or

1. A(-3, -2), B(9, 1), C(3, 6), D(5, -2)

2. A(-4, 0), B(0, 3), C(-4, -3), D(8, 6)

3. A(-10, 7), B(2, 1), C(4, 0), D(6, 1)

Angles and Parallel Lines

…Recall

When a transversal crosses parallel linesalternate interior and correspondingangles are CONGRUENT.

To prove lines parallel,

determine what type of angle pair is shown, and put them equal to each other.

Find the value of x so that the lines are parallel.

1. 5x + 5 = 45-5 -5

5x = 405

x = 8

5

2.

6x + 10 + 10x + 10 = 18016x + 20 = 180

- 2016x = 160

- 20

16x = 10

16

You try…

Find1.

the value of x so that the lines2.

are parallel.

3. 4.

You try…

Find1.

the value of x so that the lines2.

are parallel.

3. 4.