UNIT 1 PART 2

LINES IN GEOMETRY

Perpendicular Lines

Definition: Perpendicular lines are two lines that intersect to form a right angle.

The symbol used for perpendicular lines is .

4 right angles are formed. m

n

In this figure line m is perpendicular

to line n.

With symbols we denote, m n

3

Conditional Statement

Definition: A conditional statement is a statement that can be written in if-then form.“If _____________, then ______________.”

Example:

If two angles are adjacent and add up to 90 degrees, then the angles are complementary.

Continued……

4

Conditional Statement - continued

Conditional Statements have two parts:

The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.)

The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.)

The hypothesis is the given information, or the condition.

The conclusion is the result of the given information.

Three Conditional Statements

If two lines are perpendicular, then they form congruent adjacent angles.

If two lines form congruent adjacent angles, then the lines are perpendicular.The first two are converses of each other.

The converse is formed by interchanging the hypothesis and the conclusion.

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

6

Parallel Lines

Parallel lines are coplanar lines that do not intersect.Arrows are used to indicate lines are parallel.The symbol used for parallel lines is ||.

In the above figure, the arrows show that line AB is parallel to line CD.With symbols we denote, .

7

Skew Lines and Parallel Planes

Definition: Two lines are skew if they do not intersect and are not in the same plane (not coplanar). Ex:

All planes are either parallel or intersecting. Parallel planes are two planes that do not intersect.

Ex: Plane ABC and Plane EFG

8Examples:

1. Name all segments that are parallel to2. Name all segments that intersect 3. Name all segments that are skew to4. Name all planes that are parallel to plane ABC.

Answers:5. Segments BC, FG, & EH.6. Segments DH, DC, AE & AB.7. Segments CG, BF, FE, & GH.8. Plane FGH.

9

Slope of Parallel and Perpendicular Lines

The slope of the non vertical line through the points and is

m =

The slope of a vertical line is not defined.The slope of a horizontal line is zero.

Two lines are parallel if and only if they have equal slopes.

Two lines are perpendicular if and only if the product of their slopes is -1 (reciprocals and opposite signs).

10

Examples

Any line parallel to a line with slope has slope _____.

Any line perpendicular to a line with slope has slope ___.

Any line parallel to a line with slope 0 has slope _____.

Any line perpendicular to a line with undefined slope has slope.

Any line parallel to a line with slope 2 has slope _____.

0

Zero Slope

2

11

Examples:

a. (-4, 7) and (3, 7)

b. (3, -1) and (3, 2)

c. (1, -4) and (2, 5)

d. (-2, 5) and (1, -1)

Find the slope of the line through the given

points.