In this lesson you’ll learn about the concepts and procedure to construct Parallel
and Perpendicular Lines, using the earlier learning about the basics of compass &
straightedge construction and apply them as tools to build an understanding to develop
skills of higher concepts. The presentation covering such content will be done by
the instructor in own handwriting, using video and with the help of several examples with solution. (More text below video...)
(Continued from above)
You know from earlier learning that parallel lines are coplanar lines which do not
intersect and perpendicular lines are two lines that intersect to form
right angles.
The symbol for parallel lines is
and symbol for "perpendicular" is
. Further
learn the steps now and explanation how to construct them. E.g. construct a line
through a given
point, parallel to a given line.
Given: line
and a point P; construct a line through the point, parallel to the given line.
Construct: a
parallel line
Procedure and steps of construction:
• draw line AB, locate and mark point P (Figure 1).
• draw line through point P, intersecting line AB at M.
Now you can plan to construct
an angle with vertex P, congruent to the angle of intersection (Figure 2).
• center the compass at point M and draw an arc to intersect both lines. Using the
same radius of the compass, center it at point P and draw another arc (Figure 3,
4).
• set the compass radius to the distance between the two intersection points of
the first arc. Then center the compass at the point where the second arc intersects
line PM. Mark the arc intersection point O (Figure 5). Use straight edge to join P and O and draw the line.
• Conclusion: line PO is parallel to line AB (Figure 6).
Given: Line
and a point
P; construct a line through the point, perpendicular to the given line.
Construct: a line perpendicular to the given line
Procedure and steps of construction:
• draw line, containing point P (Figure 1).
• with P as center and a suitable radius draw arcs that intersect line
at two points i.e. C and D (Figure 2).
• with P as center and a suitable radius draw an arcs that intersect line
at two points i.e. C and D. Using C and D as centers and with a radius of greater
length than the used one before, draw arcs intersecting at Q (Figure 3,4).
• use straightedge to draw line
. Conclusion:
line QP is perpendicular to line
at P (Figure 5).
Proof: You’ll notice that the construction bisects straight
APB.
APQ
and
BPQ
are right angles. Thus QP is perpendicular to line
, since two lines
intersecting at right angles are perpendicular to each other.
The video above will explain more in detail about Constructing Parallel and Perpendicular
Lines, with the help of several examples.
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