Download 2. - Tapp Middle School

Angles formed by
Transversal and Parallel Lines
March 3, 2010
Warm Up 3/3/10
1. Simplify: 5 3  36   4  7 
2. Solve for m: 2  m  5   5  m  3
3. Solve for x: x  4  12
4. Multiply and simplify:
4 2
5. Simplify:
2 4
 6 12  6 8 
Warm Up 3/4/10
1. Estimate to the nearest tenth:
70
2. Find - 169
3. Simplify and subtract: 5 8  3 32
4. Find n:
 8

2 7
 8n
5. Write in standard form: 9.7 10-4
Parallel Lines
Coplanar lines that do not intersect.
m
m || n
n
Skew lines are non-coplanar, non-intersecting
lines.
q
p
The Transversal
t
Any line that
r intersects two or
more coplanar
s
lines.
When parallel lines are cut by a transversal…
t
r
1 2
4
3
5
7
Angle pair relationships
are formed.
6
8
Some angle pairs are
congruent and other
s
angle pairs are
supplementary.
Remember!
• Congruent angles have the same measure.
2  3
• Supplementary Angles are angles that have a
sum of 180 degrees.
2  8  180
Corresponding Angles
t
Corresponding angles
are congruent angles
on the same side of the
transversal.
r
1 2
4
3
5
7
6
8
s
1  5
List the other
corresponding angles
Alternate Interior Angles
t
Alternate Interior
angles are congruent
angles on opposite
sides of the transversal
and inside the parallel
lines.
r
1 2
4
3
5
7
6
8
s
3  6
List the other alternate
interior angles.
Alternate Exterior Angles
t
Alternate Exterior
angles are congruent
angles on opposite
sides of the transversal
and outside the
parallel lines.
r
1 2
4
3
5
7
6
8
s
2  7
List the other alternate
exterior angles.
Same Side Interior
t
Same side interior
angles are
supplementary angles
on the same side of the
transversal and inside
the parallel lines.
r
1 2
4
3
5
7
6
8
s
4  6  180
List the other same side
interior angles.
Same Side Exterior
t
Same side exterior
angles are
supplementary angles
on the same side of the
transversal and outside
the parallel lines.
r
1 2
4
3
5
7
6
8
s
2  8  180
List the other same side
exterior angles.
Vertical Angles
t
Vertical angles are
congruent angles
located diagonally
opposite each other.
r
1 2
4
3
5
7
6
8
s
2  3
List the other vertical
angles.
Angle 2 measures 110°. What do
the other angles measure?
1.
2.
3. 4.
5. 6.
7. 8.
58
58 ˚˚
lr
2
3
458 ˚
58˚
585˚
lw
6
7
8 58˚
lr || lw
If angle 1 = 58 ˚ then angle 5 = 58 ˚ because they are corresponding angles,
which are congruent to each other
Since angle 1 = 58 ˚ then angle 4 = 58 ˚ and since angle 5 = 58 ˚ then angle 8 = 58 ˚
because they are vertical angles, which are congruent to each other
58 ˚
lr
122˚
2
3 122 ˚
4
5
lw
6 ˚
122
7
122˚
8
lr || lw
If angle 1 = 58 ˚ then angle 2 = 122 ˚ because the two angles form a line,
which is equal to 180 ˚
Since angle 2 = 122 ˚ then angle 7 = 122 ˚ because they are Alternate
Exterior angles, which are congruent to each other.
Since angle 3 = 122 ˚ then angle 6 = 122 ˚ because they are Alternate
Interior angles, which are congruent to each other.
2
lr
1
3
4
6
5
lw
8
7
lr || lw
•Angles 3 and 4 are Same Side Angles, therefore, they are
supplementary and add up to 180 degrees.
•If angle 3 is 120 degrees, angle 4 must be 60 degrees.
7-2 Parallel and Perpendicular Lines
In the figure, line l || line m. Find the
measure of the angle.
4
m4 = 124°
Course 3
7-2 Parallel and Perpendicular Lines
In the figure, line l || line m. Find the
measure of all the angles.
Course 3
7-2 Parallel and Perpendicular Lines
Warm Up
In the figure a || b.
1. Name the angles congruent to 3.
1, 5, 7
2. Name all supplementary angels.
3. If m1 = 105° what is m3?
105°
4. If m5 = 120° what is m2?
60°
Course 3
lr || lw
lr || lw
lr || lw
lr || lw
lr || lw
Summary Question 3/3/10
Tell your neighbor:
Name the two kinds of angles that
are formed when a transversal line
crosses two parallel lines.
Summary Question 3/4/10
Tell your neighbor:
If an angle measures 45 degrees,
how can you find the measure of
the angle adjacent (next) to it?