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ATTENTION
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Remember
-- use your compass and straight edge only! |
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Parallel
-through
a point |
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Given:
Point P is off a given line
Task: Construct a line through P parallel to the given line. |
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Directions:
1. With your straightedge, draw a transversal through point
P. This is simply a straight line which runs through
P and intersects
the given line.
2. Using your knowledge of the construction COPY AN ANGLE, construct a
copy of the angle formed by the transversal and the given line such that the
copy is located UP at point P. The vertex of your copied angle will be
point P. |
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3. When the copy of the angle is complete, you will have two parallel
lines.
This new
line is parallel to the given line.
Explanation
of construction:
Since we used the construction
to copy an angle, we now have two angles of equal measure in our diagram.
In relation to parallel lines, these two equal angles are positioned in such
a manner that they are called corresponding angles. A theorem relating
to parallel lines tells us that if two lines are cut by a transversal and
the corresponding angles are congruent (equal), then the lines are parallel.
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