angle measures-parallel-lines-cut-by-a-transversal-ppt--tmi-lsn-6.01-ppt
TRANSCRIPT
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Determining Angle Measures when Parallel Lines Are Cut
by a Transversal
Today’s Lesson
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Warm-Up Activity
We will warm up today by finding angle measures.
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These are supplementary angles.
150°x
How can you find the missing angle without using a protractor?
Supplementary angles add up to 180°.
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x + 150 = 180
150°x
The supplementary angles add up to 180 degrees.
30°
x = 180 – 150 x = 30
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43°x
How can you find the missing angle without using a protractor?
These angles are vertical. Vertical angles have the same angle measure.
x = 43°
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82°
32°x
How can you find the
missing angle of the
triangle without using a protractor?What do you know about
triangles that will help you find the missing angle?
The sum of the triangle’s angles equals 180 degrees.
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82°
32°x
The sum of the
triangle’s angles
equals 180 degrees.82 + 32 + x = 180
114 + x = 180x = 180 – 114
x = 66
66°
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Today, you will focus on using patterns to find missing angles.
Whole-Class Skills Lesson
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Congruent Angles
have the same measure in degrees
43° 43°
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Parallel Lines
Are always the same distance apart.
They will never intersect.
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Transversal
A line that crosses a pair of parallel lines.
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Corresponding Angles
Angles in the same position on parallel lines cut by a transversal are congruent.
12
34
AB
CD
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Corresponding Angles1
2
34
AB
CD1A2B3C4D
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Supplementary angles add up to
180 degrees.
Vertical angles have the same angle measure.
The sum of the triangle’s angles
equals 180 degrees.
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
What types of angles do you see in this example?
Supplementary, Vertical, and Corresponding Angles
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
Can you name the corresponding angles?
Angles 1 and 5Angles 4 and 8Angles 2 and 6Angles 3 and 7
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
Can you name the vertical angles?
Angles 1 and 3Angles 4 and 2Angles 5 and 7Angles 6 and 8
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
6
Can you name some of the supplementary angles?
Angles 1 and 2Angles 2 and 3Angles 3 and 4Angles 4 and 1
Angles 5 and 6Angles 6 and 7Angles 7 and 8Angles 5 and 8
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Lines a and b are parallel.
a
b
c
110 2
34
5
78
6
If Angle 1 measures 110 degrees, what is the measure of Angle 3?
110°
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Lines a and b are parallel.
a
b
c
110 2
34
5
78
6
If Angle 1 measures 110 degrees, what is the measure of Angle 4?
70°
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Lines a and b are parallel.
a
b
c
110 2
34
5
78
6
If Angle 1 measures 110 degrees, what is the measure of Angle 8?
70°
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Lines a and b are parallel.
a
b
c
110 2
34
5
78
6
If Angle 1 measures 110 degrees, what is the measure of Angle 7?
110°
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
52°
If Angle 6 measures 52 degrees, what is the measure of Angle 7?
128°
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Lines a and b are parallel.
a
b
c
1 2
34
5
78
52°
If Angle 6 measures 52 degrees, what is the measure of all the angles on the diagram?
128°
128° 52°
52°
128°
52° 128°