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Slope and Parallel Lines

- Sections 4.5 4.6

Definitions

- A plane is a surface such that if any two points

on the surface are connected by a line, all

points of the line are also on the surface. - A plane has only two dimensions length and

width but no thickness.

Definitions

- If points, lines, segments, and so forth lie in

the same plane, we call them coplanar. - Points, lines, segments, and so forth that do not

lie in the same plane are called noncoplanar.

Definitions

- A transversal is a line that intersects two

coplanar lines in two distinct points.

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Definitions

- In the diagram, the region between lines d and e

is the interior of the figure. - In the diagram, the rest of the plane except the

region between lines d and e is the exterior of

the figure.

Definitions

- Alternate Interior Angles are a pair of angles

formed by two lines and a transversal. The angles

must - both lie in the interior of the figure,
- lie on alternate sides of the transversal,
- have different vertices.

Definitions

- Alternate Exterior Angles are a pair of angles

formed by two lines and a transversal. The angles

must - both lie in the exterior of the figure,
- lie on alternate sides of the transversal,
- have different vertices.

Definitions

- Corresponding Angles are a pair of angles formed

by two lines and a transversal. - One angle must lie in the interior of the figure,

and the other must lie in the exterior. - The angles must lie on the same side of the

transversal but have different vertices.

corr. angles

alt. ext. angles

alt. int. angles

corr. angles

vert. angles

corr. angles

alt. ext. angles

alt. int. angles

Name the pairs of...

Parallel Lines

- Parallel () lines are two coplanar lines which

do not intersect. - Parallel lines have the same slope.

Slope Review ?

- The slope of a nonvertical line (or segment or

ray) containing points (x1, y1) and (x2, y2) is

defined by - Find the slope of the line containing points (2,

-1) and (7, 4)

Remember,

- Rising line positive slope
- Falling line negative slope
- Horizontal line zero slope
- Vertical line no slope (undefined slope)

Slopes of Parallel Lines

- Theorem 26 If two nonvertical lines are

parallel, then their slopes are equal. - Theorem 27 If the slopes of two nonvertical

lines are equal, then the lines are parallel.

Note You do NOT need to prove these theorems!!

Slopes of Perpendicular Lines

Note You do NOT need to prove these theorems!!

- Theorem 28 If two nonvertical lines are

perpendicular, then each lines slope is the

opposite reciprocal of the others. - Theorem 29 If a lines slope is the opposite

reciprocal of another lines slope, then the two

lines are perpendicular.

Flip the top and bottom of fraction and change to

opposite sign!