Constructions: Parallel Lines · 2019. 9. 18. · Parallel Lines 2 Now we’ll construct two...
Transcript of Constructions: Parallel Lines · 2019. 9. 18. · Parallel Lines 2 Now we’ll construct two...
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Constructions: Parallel Lines
Objectives:
1. To construct parallel lines with a compass
and a straightedge using the equidistant
method and the Corresponding Angles
Postulate
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Definition
Parallel lines are lines that lie in the same plane and do not intersect.
If two lines in a plane are parallel, then they must always be the same distance apart. The converse of this is also true. This gives you a way, called the equidistant method, of constructing parallel lines.
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Parallel Lines 1
1. Draw a line m
and a point P not
on m.
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Parallel Lines 1
2. Draw a line
perpendicular to
line m through
point P. Label
the point of
intersection Q. (This was a
construction from the
previous presentation)
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Parallel Lines 1
3. Draw a point R
on the line to the
right of Q.
Construct a line
n through point R
that is
perpendicular to
line m. (This was also
a construction from the
previous presentation)
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Parallel Lines 1
4. Construct point
S on line n by
copying segment
QP onto line n,
with Q
corresponding to
R and P
corresponding to
S.
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Parallel Lines 1
5. Draw a line
through P and S.
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Parallel Lines 2
Now we’ll construct two parallel lines using a
different method. This construction relies upon
the Converse of the Corresponding Angles
Postulate; that is,
if our corresponding
angles are
congruent, then
the lines will be
parallel.
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Parallel Lines 2
1. Draw line l and
point P not on l.
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Parallel Lines 2
2. Draw a
transversal
through point P
intersecting line l.
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Parallel Lines 2
3. Copy the angle
formed by the
transversal and
line l at point P.
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Parallel Lines: Video
Click on the
image to
watch a
video of the
construction.
©2001 New York State Regents Exam Prep Center
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Assignment
“Just Your Basic
Constructions
Worksheet:
• Parallel Lines 1 and 2
• Now on to the
“Construction
Problems” Worksheet