Transcript PARALLEL LINES CUT BY A TRANSVERSAL

PARALLEL LINES CUT BY A
TRANSVERSAL
DEFINITIONS
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PARALLEL
TRANSVERSAL
ANGLE
VERTICAL ANGLE
CORRESPONDING ANGLE
ALTERNATE INTERIOR ANGLE
ALTERNATE EXTERIOR ANGLE
DEFINITIONS
• SUPPLEMENTARY ANGLE
• COMPLEMENTARY ANGLE
• CONGRUENT
Parallel lines cut by a transversal
2
3
6
7 8
5
1
4
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 1 and < 2 are called SUPLEMENTARY ANGLES
They form a straight angle measuring 180 degrees.
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
Name other supplementary pairs:
< 2 and < 3
< 3 and < 4
< 4 and < 1
< 5 and < 6
< 6 and < 7
< 7 and < 8
< 8 and < 5
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 1 and < 3 are called VERTICAL ANGLES
They are congruent m<1 = m<3
Parallel lines cut by a transversal
2
3
6
7 8
1
4
5
< 2 and < 4
< 6 and < 8
Name other vertical pairs:
< 5 and < 7
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 1 and < 5 are called CORRESPONDING ANGLES
They are congruent
m<1 = m<5
Corresponding angles occupy the same position on the top and
bottom parallel lines.
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 2 and < 6
< 3 and < 7
Name other corresponding pairs:
< 4 and < 8
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 4 and < 6 are called ALTERNATE INTERIOR ANGLES
They are congruent
m<4 = m<6
Alternate Interior on on the inside of the two parallel lines and
on opposite sides of the transversal.
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
Name other alternate interior pairs:
< 3 and < 5
Parallel lines cut by a transversal
2
3
6
1
4
5
7 8
< 2 and < 8
Name other alternate exterior pairs:
< 1 and < 7
TRY IT OUT
2
3
6
1
4
5
7 8
The m < 1 is
60 degrees.
What is the m<2 ?
120 degrees
TRY IT OUT
2
3
6
1
4
5
7 8
The m < 1 is
60 degrees.
What is the m<5 ?
60 degrees
TRY IT OUT
2
3
6
1
4
5
7 8
The m < 1 is
60 degrees.
What is the m<3 ?
60 degrees
TRY IT OUT
120 60
60 120
120
60
60 120
TRY IT OUT
2x + 20
What do you know about the angles?
Write the equation.
Solve for x.
x + 10
SUPPLEMENTARY
2x + 20 + x + 10 = 180
3x + 30 = 180
3x = 150
x = 30
TRY IT OUT
3x - 120
2x - 60
What do you know about the angles? ALTERNATE INTERIOR
Write the equation.
Solve for x.
Subtract 2x from both sides
Add 120 to both sides
3x - 120 = 2x - 60
x
=
60
WEBSITES FOR PRACTICE
Ask Dr. Math: Corresponding /Alternate Angles
Project Interactive: Parallel Lines cut by Transversal