parallel lines and angles

Parallel Lines Parallel Lines and Anglesand Angles

Parallel Lines Parallel Lines and Anglesand Angles

Parallel Lines and PlanesParallel Lines and Planes

You will learn to describe relationships among lines, parts of lines, and planes.

In geometry, two lines in a plane that are always the same distance apart are ____________.parallel lines

No two parallel lines intersect, no matter how far you extend them.

Parallel Lines and PlanesParallel Lines and Planes

Definition of

Parallel

Lines

Two lines are parallel if they are in the same plane and do not ________. -This means the lines never touch-This means the lines have the same slope-This means the lines are always the same distance apart

-The symbol for parallel is two vertical lines (II). For example if line m and line t are parallel you could write m II t.

intersect

On your paper: #1. What are three ways to describe how lines are parallel? #2. What is the symbol for parallel?

Parallel Lines and TransversalsParallel Lines and Transversals

You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel linesand a transversal.

Parallel Lines and TransversalsParallel Lines and Transversals

In geometry, a line, line segment, or ray that intersects two or more lines atdifferent points is called a __________transversal

l

m

B

A

AB is an example of a transversal. It intercepts lines l and m.

Note all of the different angles formed at the points of intersection.

1 2

34

5

76

8

Parallel Lines and TransversalsParallel Lines and Transversals

Definition of

Transversal

In a plane, a line is a transversal if it intersects two or more

lines, each at a different point.

The lines cut by a transversal may or may not be parallel.

l

m

1 2

34

576

8

ml

Parallel Lines

t is a transversal for l and m.

t

1 234

5

7

6

8

b

c

cb ||

Nonparallel Lines

r is a transversal for b and c.

r

Parallel Lines and TransversalsParallel Lines and Transversals

Two lines divide the plane into three regions.

The region between the lines is referred to as the interior.

The two regions not between the lines is referred to as the exterior.

Exterior

Exterior

Interior

l

m

1 2

34

576

8

Parallel Lines and TransversalsParallel Lines and Transversals

When a transversal intersects two lines, _____ angles are formed.eight

These angles are given special names.

tInterior angles lie between thetwo lines.

Exterior angles lie outside thetwo lines.

Alternate Interior angles are between the two lines on the opposite sides of the transversal.

Consectutive Interior angles between the two lines are on the same side of the transversal.

Alternate Exterior angles areoutside the two lines on the opposite sides of thetransversal.

Parallel Lines and TransversalsParallel Lines and Transversals

Alternate

Interior

Angles

If two parallel lines are cut by a transversal, then each pair of

Alternate interior angles is _________. (equal)

Angles 4 and 6 are alternate interior angles so we know

1 234

57

68

64

congruent

On your paper: #3. Write down one other pair of alternate interior angles.

Parallel Lines and TransversalsParallel Lines and Transversals

1 2

34

576

8

Consecutive

Interior

Angles

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is _____________. (add to 180)

Angles 4 and 5 are consecutive interior angles so we know:

supplementary

18054

On your paper: #4. Write down one other pair of consecutive interior angles.

Parallel Lines and TransversalsParallel Lines and Transversals

1 2

34

576

8

Alternate

Exterior

Angles

If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is _________.

Angle 1 and 7 are alternate exterior angles so we know:

congruent

71

On your paper: #5. Write down one other pair of alternate exterior angles.

Transversals and Corresponding AnglesTransversals and Corresponding Angles

You will learn to identify the relationships among pairs of corresponding angles formed by two parallel lines and a transversal.

Transversals and Corresponding AnglesTransversals and Corresponding Angles

l

m

1 2

34

576

8

t

When a transversal crosses two lines, the intersection creates a number ofangles that are related to each other.

Note 1 and 5 below. Although one is an exterior angle and the other is an interior angle, both lie on the same side of the transversal.

Angle 1 and 5 are called __________________. So <1=<5corresponding angles

On your paper: #6. Write down three pairs of corresponding angles?

Transversals and Corresponding AnglesTransversals and Corresponding Angles

Corresponding

AnglesIf two parallel lines are cut by a transversal, then each pair of corresponding angles is _________.congruent

Transversals and Corresponding AnglesTransversals and Corresponding Angles

Concept

Summary

Congruent Supplementary

alternate interior

alternate exterior

corresponding

consecutive interior

Types of angle pairs formed when a transversal cuts two parallel lines.

Turn in your half piece of paper. Go to a table and complete your notesheet page on parallel lines. After you have completed this, start the next sheet in your packet. Whatever you don’t complete is homework for tonight.