parallel lines and angles
DESCRIPTION
Parallel Lines and Angles. Parallel Lines and Planes. What You'll Learn. 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. - PowerPoint PPT PresentationTRANSCRIPT
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.