Complimentary Angles, Supplementary Angles, and Parallel Lines

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Complimentary Angles, Supplementary Angles, and
Parallel Lines
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Adjacent angles are side by side and share a
common ray.
15º
45º
3
These are examples of adjacent angles.
45º
80º
35º
55º
50º
130º
85º
20º
4
These angles are NOT adjacent.
100º
50º
35º
35º
45º
55º
5
When 2 lines intersect, they make vertical angles.
75º
105º
105º
75º
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Vertical angles are opposite one another.
75º
105º
105º
75º
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Vertical angles are congruent (equal).
30º
150º
150º
30º
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Supplementary angles add up to 180º.
40º
60º
120º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
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Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
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Parallel Lines and Planes
What You'll Learn
You will learn to describe relationships among
lines, parts of lines, and planes.
In geometry, two lines in a plane that are always
the same distance apart are ____________.
parallel lines
No two parallel lines intersect, no matter how
far you extend them.
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Parallel Lines and Planes
Definition of Parallel Lines Two lines are parallel if they are in the same plane and do not ________.
intersect
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Parallel Lines and Transversals
In geometry, a line, line segment, or ray that
intersects two or more lines at different points
is called a __________
transversal
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1
3
4
5
6
8
7
Note all of the different angles formed at the
points of intersection.
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Parallel Lines and Transversals
Definition of Transversal In a plane, a line is a transversal if it intersects two or more lines, each at a different point.
The lines cut by a transversal may or may not be
parallel.
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Parallel Lines and Transversals
Two lines divide the plane into three regions.
The region between the lines is referred to as
the interior.
The two regions not between the lines is referred
to as the exterior.
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Parallel Lines and Transversals
When a transversal intersects two lines, _____
angles are formed.
eight
These angles are given special names.
t
Interior angles lie between the two lines.
Exterior angles lie outside the two lines.
Alternate Interior angles are on the opposite
sides of the transversal.
Alternate Exterior angles are on the opposite
sides of the transversal.
Consecutive Interior angles are on the same side
of the transversal.
?
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Parallel Lines and Transversals
Theorem 4-1 Alternate Interior Angles If two parallel lines are cut by a transversal, then each pair of alternate interior angles is _________.
congruent
2
1
3
4
5
6
7
8
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Parallel Lines and Transversals
Theorem 4-2 Consecutive Interior Angles If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is _____________.
supplementary
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Parallel Lines and Transversals
Theorem 4-3 Alternate Exterior Angles If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is _________.
congruent
?
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Transversals and Corresponding Angles
When a transversal crosses two lines, the
intersection creates a number ofangles that are
related to each other.
Note ?1 and ?5 below. Although one is an
exterior angle and the other is an interior
angle, both lie on the same side of the
transversal.
corresponding angles
Angle 1 and 5 are called __________________.
Give three other pairs of corresponding angles
that are formed
?4 and ?8
?3 and ?7
?2 and ?6
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Transversals and Corresponding Angles
Postulate 4-1 Corresponding Angles If two parallel lines are cut by a transversal, then each pair of corresponding angles are _________.
congruent
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Transversals and Corresponding Angles
Concept Summary
Concept Summary Congruent Supplementary
Types of angle pairs formed when a transversal
cuts two parallel lines.
consecutive interior
alternate interior
alternate exterior
corresponding
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Transversals and Corresponding Angles
s t and c d. Name all the angles that
arecongruent to ?1. Give a reason for each
answer.
corresponding angles
?3 ? ?1
vertical angles
?6 ? ?1
alternate exterior angles
?8 ? ?1
corresponding angles
?9 ? ?1
alternate exterior angles
?14 ? ?1
corresponding angles
?11 ? ?9 ? ?1
corresponding angles
?16 ? ?14 ? ?1