Embed Size (px)
Citation preview
Parallel Lines Parallel Lines and Anglesand Angles
Parallel Lines Parallel Lines and Anglesand Angles
Vertical Angles
• Vertical Angles are angles that are opposite each other at an intersection.
• Vertical Angles are equal
1
2 3
4
Angles 1 and 4 are vertical angles
Angles 2 and 3 are vertical anglesOn your notesheet: Write a word and a picture definition for vertical angles.
Supplementary Angles• Supplementary angles are angles that
form lines (also called linear pairs)• Supplementary angles add up to 180
1 2
3 4
On your notesheet: Write a word and a picture definition for supplementary angles.
Angles 1 and 2 are supplementary, Angles 1 and 3 are supplementaryAngles 2 and 4 are supplementary, Angles 3 and 4 are supplementary
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 notesheet: Write a verbal and picture definition of parallel linesOn 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.
t
Corresponding angles are in the same positionat each intersection. Ex. 1 and 5, 2 and 6,4 and 8, 3 and 7
Alternate Interior angles are between the two lines on the opposite sides of the transversal. Ex. 4 and 6, 3 and 5
Consectutive Interior angles between the two lines are on the same side of the transversal. Ex. 4 and 5, 3 and 6
Alternate Exterior angles are outside the two lines on the opposite sides of thetransversal. Ex. 1 and 7, 2 and 8
Parallel Lines and TransversalsParallel Lines and Transversals
Alternate
Interior
Anglesbetween the two lines on the opposite sides of the transversal. Ex. 4 and 6,
3 and 5
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
Anglesbetween the two lines are on the same side of the transversal. Ex. 4 and 5,
3 and 6
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
Anglesoutside the two lines on the opposite sides of thetransversal. Ex. 1 and 7,
2 and 8
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.
Parallel Lines and TransversalsParallel Lines and Transversals
Corresponding
Anglesare in the
same positionat each
intersection. Ex. 1 and 5,
2 and 6,4 and 8, 3 and 7
If two parallel lines are cut by a transversal, then each pair of corresponding angles is _________.
Angle 1 and 5 are both in the upper left of each intersection so they are corresponding angles and we then know angle 1=angle 5
congruent
On your paper: #6. Write down three other pairs of corresponding angles.
l
m
1 2
34
576
8
t
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.
On your notesheet: Under “Special pair of Angles” for each pair write equal or supplementary, then using the examples on the notesheet write one pair from A and B.
