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Angles and Parallel Lines
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Slide 1
Angles and Parallel Lines
Angles and Parallel Lines
Duration: 00:00:10
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Slide 2
Parallel Lines
Parallel Lines
Duration: 00:00:47
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• Lines that are coplanar and NEVER intersect.
– Remember that COPLANAR means on the same plane
These are two parallel lines.
They will keep extending in both
directions and never intersect.
B
A
AE, DH, CG, BF would all be parallel to each other.
AB, DC, HG, EF would all be parallel to each other.
C
D
E
H
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AD, BC, FG, EH would all be parallel to each other.
F
G
Notes:
In this module, you will learn about two different
types of lines, parallel and skew. You will also
be introduced to four new angle pairs and their
properties.
Notes:
Parallel lines are lines that are coplanar and that
never intersect. If you recall, coplanar lines were
lines that were on the same plane. Never
intersect means that the lines will never cross. In
the first picture, the two lines will keep extending
indefinitely and will never cross, so they will be
defined as parallel lines. In the three
dimensional box, there are three sets of parallel
lines. AB, DC, GH, and EF (the lines in green)
are all parallel lines. AD, BC, EH, and GF (the
lines in blue) would all be parallel lines. AE, BF,
CG, and DH (the lines in red) are all parallel
lines.
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Slide 3
Notes:
Parallel Lines
There are two symbols to know for parallel lines.
One is for written instructions. That is the first
symbol. Two small lines that are parallel written
between two lines means parallel. The other
symbol is for pictures. When there are arrows on
the lines, it means the lines are parallel. If there
is one arrow on the line, it would be parallel to
any other line with one arrow. If there are two
arrows on a line, it would be parallel to a line with
two arrows, etc.
Duration: 00:00:31
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Slide 4
Duration: 00:00:26
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Notes:
Skew Lines
Skew Lines
• Lines that are NON-coplanar that NEVER intersect.
– Remember that NON-coplanar means not on the same plane.
B
A
DC and GF would be skew lines.
C
D
AE and HG would be skew lines.
E
F
H
Slide 5
You try….
Duration: 00:00:06
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G
You try….
1.
2.
3.
4.
5.
6.
Name a line parallel to XY.
Name a line parallel to WS.
Name a line parallel to UT.
Name a line skew to YZ.
Name a line skew to XR.
Name a line skew to UR.
Notes:
You try these examples. See the last slide in the
presentation to check your answers.
W
X
Z
Y
R
U
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Another type of line that will never intersect is
skew lines. Skew lines are NON-coplanar lines
that will never intersect. Since they are noncoplanar, that means they are not on the same
plane. AE and HG (lines in blue) are an example
of skew lines. DC and GF (lines in red) are an
example of skew lines. Can you come up with
any other examples?
S
T
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Slide 6
Transversal
Transversal
Duration: 00:00:13
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• A line that intersects at least two other lines in two distinct
points.
transversal
Slide 7
Alternate Interior Angles
Duration: 00:00:18
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Alternate Interior Angles
• A pair of angles that are on opposite sides of the transversal
but inside the two lines.
transversal
1
3
5
2
4
A transversal is a line that intersects two or more
other lines in distinct points. When a
transversals intersects lines it creates some new
angle pairs. Proceed in the presentation to learn
these new angle pairs.
Notes:
Alternate interior angles are a pair of angles that
are on opposite sides of the transversal, and are
inside the two lines. Opposite makes them
alternate, while being inside makes then interior.
When the two lines are parallel, alternate interior
angles are always CONGRUENT.
6
3 and 6 would be alternate interior angles.
8
7
Notes:
4 and 5 would be alternate interior angles.
• When the two lines are parallel, then alternate interior angles
are CONGRUENT.
Slide 8
Alternate Exterior Angles
Duration: 00:00:24
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Alternate Exterior Angles
• A pair of angles that are on opposite sides of the transversal
but outside the two lines.
transversal
1
3
5
7
2
4
6
8
1 and 8 would be alternate exterior angles.
Notes:
Alternate exterior angles are a pair of angles that
are on opposite sides of the transversal and are
outside the two lines. Like alternate interior
angles, they are on opposite sides of the
transversals, but unlike alternate interior angles,
alternate exterior angles are outside the two
lines. When the two lines are parallel, alternate
exterior angles are always CONGRUENT.
2 and 7 would be alternate exterior angles.
• When the two lines are parallel, then alternate exterior angles
are CONGRUENT.
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Slide 9
Corresponding Angles
Duration: 00:00:18
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Corresponding Angles
• A pair of angles that sit in the same corner of the transversal
but on a different line.
transversal
1 and 5 would be corresponding angles.
1
3
5
2 and 6 would be corresponding angles.
2
4
6
8
7
3 and 7 would be corresponding angles.
Notes:
Corresponding angles are a pair of angles that
are on the same corner of the transversal but are
on different lines. Corresponding angle pairs
also have one angle that is interior and one
angle that is exterior. When the two lines are
parallel, corresponding angles are always
CONGRUENT.
4 and 8 would be corresponding angles.
• When the two lines are parallel, then corresponding angles
are CONGRUENT.
Slide 10
Consecutive Interior Angles
Duration: 00:00:22
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Consecutive Interior Angles
• A pair of angles that are inside the lines and on the same side
of the transversal.
• Also called same-side interior angles.
transversal
1
3
5
7
2
4
6
3 and 5 would be cosecutive angles.
8
Notes:
Consecutive interior angles are a pair of angles
that are on the same side of the transversal and
are inside the two lines, making then interior.
Because they are on the same side of the
transversal, consecutive interior angles may also
be called same-side interior angles. When the
two lines are parallel, consecutive interior angles
are SUPPLEMENTARY.
4 and 6 would be consecutive angles.
• When the two lines are parallel, then consecutive angles are
SUPPLEMENTARY.
Slide 11
Examples
Duration: 00:01:15
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Examples
Find the measure of angle 1.
1.
2.
56
1
1
91
3.
4.
134
1
85
1
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Notes:
1. These are corresponding angles
because they sit in the same corner of
the transversals (upper right side) but
are on different lines. When lines are
parallel, corresponding angles are
congruent, so angle 1 = 56°.
2. These are consecutive interior angles
because they sit on the same side of the
transversal (the bottom side) and they
are inside the lines. When lines are
parallel, consecutive angles are
supplementary, which means they add to
equal 180°, so angle 1 = 89°.
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3. These are alternate interior angles
because they sit on opposite sides of the
transversal (one on the top, one on the
bottom) and they are inside the lines.
When lines are parallel, alternate interior
angles are congruent, so angle 1 = 85°.
4. These are alternate exterior angles
because they sit on opposite sides of the
transversal (one on the left, one on the
right) and they are on the outside of the
lines. When lines are parallel, alternate
exterior angles are congruent, so angle 1
= 134°.
Slide 12
You try….
Find the measure of angle 1.
You try….
Find the measure of angle 1.
1.
2.
Duration: 00:00:05
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Notes:
You try these examples. See the last slide in the
presentation to check your answers.
81
75
1
1
3.
4.
155
101
1
1
Slide 13
You try…
Duration: 00:00:05
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You try…
Find x.
1.
2.
Notes:
You try these examples. See the last slide in the
presentation to check your answers.
Find the measure of the angle in bold.
3. Bold angle is bottom angle. 4. Bold angle is top angle.
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Slide 14
Solutions
Duration: 00:00:05
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Slide 15
Answers to You Try slides…
Duration: 00:00:09
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1. 87 = 7x + 10
- 10
- 10
77 = 7x
7
7
x = 11
2. 75 = 8x + 11
- 11
- 11
64 = 8x
8
8
x=8
3. 22x + 4 + 35x + 5 = 180
57x + 9 = 180
-9
-9
57x = 171
57
57
x=3
35x + 5 = 35(3) + 5 = 110
4. 14x + 4 + 6x – 4 = 180
20x = 180
20
20
x=9
These are the solutions to the problems on the
previous you try slide.
14x + 4 = 14(9) + 4 = 130
Answers to You Try slides…
Parallel/Skew Lines
1. WZ, ST, RU
2. ZT, YU, XR
3. RS, XW, YZ
4. XR, WS, RU, ST
5. YZ, UT, WZ, ST
6. YZ, WX, ZT, WS
Notes:
Angles
1. 105
2. 81
3. 155
4. 101
Notes:
Here are the answers to each of the you try
slides. I hope you did well. After you have
completed this presentation, proceed with the
Check Your Knowledge activity.
Find x.
1. 11
2. 8
Find the angle in bold.
3. 110
4. 130
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