Download Parallel Lines

Today’s Lesson
8.G.5. Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when parallel
lines are cut by a transversal, and the angle
criterion for similarity of triangles.
Goals
By the end of the unit, I will….
» Be able to identify different types of angles
and lines.
» Use arguments to establish facts about angle
sums and exterior angles of triangles.
» Identify the angles created when parallel
lines are cut by a transversal.
» Create arguments for the similarity of
triangles based on angles.
Parallel Lines
Lines in a plane that never intersect.
Transversal
A line that crosses two or more other lines.
Complementary Angles
Two angles that equal 90 degrees.
Supplementary Angles
Two angles that equal 180 degrees.
x
150°
These are supplementary angles.
Supplementary angles add up to 180°.
The supplementary angles add up to 180
degrees.
x
150°
180 - 50 = x
x = 30
30°
Interior Angles
Angles formed by a transversal and the lines it
crosses, inside the parallel lines.
Exterior Angles
Angles formed by a transversal and the lines it
crosses, outside the parallel lines.
Alternate Angles
Two angles formed by a transversal and the lines it crosses,
on opposite sides of the transversal. Alternate angles have
the same measurement.
Corresponding Angles
Two angles on the same side of the transversal, on a different
line. Corresponding angles have the same measurement.
1
2
4
3
A
B
D
C
Corresponding Angles
1
2
4
3
A
B
D
C
Vertical Angles
Two angles that share a vertex but not a side. Vertical angles
have the same measurement.
43°
x
These angles are vertical.
Vertical angles have the same angle measure.
Lines a and b are parallel.
c
110
a
4
5
b
8
2
3
6
7
If Angle 1 measures 110 degrees,
what is the measure of Angle 3?
110°
Lines a and b are parallel.
c
110
a
4
5
b
8
2
3
6
7
If Angle 1 measures 110 degrees,
what is the measure of Angle 4?
70°
Lines a and b are parallel.
c
110
a
4
5
b
8
2
3
6
7
If Angle 1 measures 110 degrees,
what is the measure of Angle 8?
70°
Lines a and b are parallel.
c
110
a
4
5
b
8
2
3
6
7
If Angle 1 measures 110 degrees,
what is the measure of Angle 7?
110°
Lines a and b are parallel.
c
1
a
4
5
b
8
2
3
52°
7
If Angle 6 measures 52 degrees,
what is the measure of Angle 7?
128°
Lines a and b are parallel.
c
128°
1
a
4
52°
b
128°
52°
5
8
2
3
52°
128°
52°
7
128°
If Angle 6 measures 52 degrees, what is the
measure of all the angles on the diagram?