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Math
A |
Angles with Parallel Lines |
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Angles formed by parallel lines
and transversals
(lines intersecting the set of parallel lines),
have very interesting relationships
and very interesting names.
The most important angles needed
for Math A are called alternate interior
angles, alternate exterior
angles and corresponding
angles. |
Certain angle "names" describe
"where" the angles are located.
Remember that:
- the word
INTERIOR means
BETWEEN the parallel lines.
- the word
EXTERIOR means
OUTSIDE the parallel
lines.
- the word
ALTERNATE means
"alternating sides" of the transversal.
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Alternate Interior
Angles
 (measures
are equal)
These angles are "friendly"
because
their name clearly describes "where"
they are located. |
Look carefully at the diagram
below: |
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Hint: If you
draw a Z on the diagram, the alternate interior angles
are found in the corners of the Z. The Z may also be a backward Z.
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Alternate Exterior
Angles
(measures
are equal)
These angles are also "friendly"
because
their name clearly describes "where"
they are located. |
Look carefully at the diagram
below:
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Corresponding Angles
(measures
are equal)
Unfortunately, the name of these
angles
does not clearly indicate "where" they
are located. They are located:
- on the SAME SIDE of the transversal
- one INTERIOR and one EXTERIOR
- and they are NOT adjacent (they don't touch).
(They lie on the same side of the
transversal,
in corresponding positions.) |
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Hint: If you
took a picture of one corresponding angle and slid
the angle up (or down) the same side of the transversal, you
would arrive at the other corresponding angle.
Also: If you
draw an F on the diagram, the corresponding angles can be
found in the "corners" of the F. The F may be backward and/or
upside-down.
Of course, there are also other angle
relationships occurring with parallel lines.
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Vertical Angles
(measures
are equal)
Vertical angles are ALWAYS equal, whether you
have parallel
lines or not. |
Refresh your memory using the diagram below: |
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Interior Angles on the
Same Side of the Transversal
(measures
are supplementary)
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You don't need to remember these angles
by name, but
you do need to know how they are related to one another: |
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Adjacent Angles creating
a Straight Line
(measures
are supplementary) |
This is an
"old" idea about angles revisited. Since a
straight angle contains 180º, these two adjacent angles
add to 180.
(Adjacent angles share a vertex, share a side, and do not
overlap.) |
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