In this lesson youll learn about the concepts and procedure of performing the basic
constructions. 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. In these constructions compass and straightedge are used for repeated
application of five basic constructions making use of the constructed
points,
lines
and
circles. (More text below video...)
(Continued from above) These are:
creating the line through two existing points.
using centre point, create the circle through a point.
create the point which is the intersection of two existing, nonparallel lines.
create one or two points in the intersection of a line and a circle (provided
they intersect).
creating one or two points in the intersection of two circles (provided they intersect).
With above basics in mind, walk through the explanation taking an example now. Generally
the procedure is: the point of compass is fixed as the
center of a circle and the
pencil point draws an arc i.e. a part of the circle. If you keep the
distance between
the points of compass pair, all the arcs drawn are arcs of congruent circles. Notice
that all line segments originating from the center to a point on an arc represent
radii of congruent circles. To prove that the construction is valid, you may use
the related postulate "Radii of congruent circles are congruent".
For Example: Given to construct a line segment congruent to a given line
segment line
Given:
Construct: A line segment,
congruent to
with a straightedge,
draw line, , and mark a point P on it.
on ,
place the compass so that its point is at A and the pencil point at B.
maintaining the setting of compass, place the point at P and draw an arc intersecting
at
D.
It concludes to:
Proof: Construction performed makes
at
D.
It concludes to:
,
because
and
are radii of congruent circles.
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