Transcript 3.3 Parallel Lines & Transversals

Parallel Lines,
Transversals,
&
Special Angle
Pairs
When 2 lines intersect
crazy, wonderful
things happen!
When 2 lines,
rays or
segments
intersect, 4
angles are
created.
1
4
2
3
Angles 1 & 4 are a linear pair = 180°
Angles 1 & 2 are a linear pair = 180°
Angles 2 & 3 are a linear pair = 180°
Angles 3 & 4 are a linear pair = 180°
Angles 1 & 3 are VERTICAL ANGLES and are congruent.
Angles 4 & 2 are VERTICAL ANGLES and are congruent.
Transversal
A line, ray, or segment that intersects
2 or more
COPLANAR lines, rays, or segments.
Check out the new notation!!
The extra set of arrows tell us the
lines are parallel.
Parallel
lines
transversal
Non-Parallel
lines
transversal
INTERIOR
–The space INSIDE the 2 lines
interior
EXTERIOR
-The space OUTSIDE the 2 lines
exterior
exterior
Special Angle
Relationships
Interior Angles
<3 & <6 are Alternate Interior angles
<4 & <5 are Alternate Interior angles
<3 & <5 are Same Side Interior angles
<4 & <6 are Same Side Interior angles
Exterior Angles
1
3 4
5 6
7 8
2
<1 & <8 are Alternate Exterior angles
<2 & <7 are Alternate Exterior angles
<1 & <7 are Same Side Exterior angles
<2 & <8 are Same Side Exterior angles
Corresponding Angles
Angles that are in the same position on both
lines
<1 & <5 are Corresponding angles
<2 & <6 are Corresponding angles
<3 & <7 are Corresponding angles
<4 & <8 are Corresponding angles
$
Let’s Practice
Naming Angle Pairs
1 2
3 4
5 6
7
8
$
1. Name a pair of alternate
interior angles
2. Name a pair of same side
exterior angles
3. Name a pair of same side
interior angles
4. Name a pair of alternate
exterior angles
5. Name a linear pair
6. Name a pair of vertical angles
7. Name a pair of corresponding
angles
8. Name another pair of
corresponding angles
9. Name a linear pair
10. Name a pair of vertical angles
Special Angle Measurement
Relationships
WHEN THE LINES ARE
♥Alternate Interior Angles
PARALLEL
are CONGRUENT
1
3
5
2
4
6
7 8
If the lines are not parallel,
these measurement
relationships
DO NOT EXIST.
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
♥ Corresponding angles are
CONGRUENT
Let’s look closer
Please get:
♥straight edge
♥protractor
♥piece of paper
1. Using both sides of the
straight edge and a
pencil, create a pair of
parallel lines
2. Draw a transversal
3. Using the protractor,
measure all the angles
4. On the same paper, create
a pair of non-parallel lines
5. Draw a transversal
6. Using the protractor,
measure all the angles
What did you
discover
about angle
measures?
12
34
56
7 8
1
2
3
4
5
When lines are not parallel,
special angle pairs do not have
a measurement relationship.
6
7
8
When lines are parallel,
measurement relationships
exist.
Angle pairs always keep the
same names regardless if
the lines are parallel.
Let’s Practice
120°1
60°3
120° 5
7
60°
2 60°
4 120°
6 60°
8 120°
m<1=120°
Find all the remaining angle
measures AND give the name of
the special angle pair.
m<1=91°
Find all the remaining angle measures
AND give the name of the special
angle pair.
89°
91°1 2
89° 3 491°
WE DON’T
KNOW!
5 6
7 8
Vocabulary
Parallel lines: Lines that are always
equidistant from each other – they will
never intersect. (2D or 3D)
Perpendicular lines: Lines that intersect at a
90◦ angle. (2D or 3D)
Skew lines: Lines that are not parallel but
will never intersect. (3D only)
Use the diagram to name each of the following.
1. A pair of parallel planes
2. All lines that are parallel to
3. Four lines that are skew to
4. All lines that are parallel to plane QUV
5. A plane parallel to plane QUW
Identify all pairs of each type of
angle in the diagram below right.
1.
2.
3.
4.
Corresponding angles
Same-side interior angles
Alternate interior angles
Alternate exterior angles
Find the value of x and y. Then find the measure of each
labeled angle.
♥What kind of angles are these?
♥What is their measurement
relationship?
♥How shall we set up the
equation?
♥Do it.
x + x – 26 = 180
2x = 206
x = 103
Are we done?
Angle measures are
103 ◦ and 77◦
Another practice problem
40°
120°
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
Assignment
Practice 3.1
and 3.2