Geometry: Getting Started - Basic Constructions
This is a free lesson from our course in Geometry
 
   
In this lesson you’ll 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...)
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Other useful lessons:
Angle Bisectors and Perpendicular Bisectors
Constructing Parallel and Perpendicular Lines
Midpoint of a Line Segment
(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, non-parallel 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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