Tuesday, July 13, 2010

STRAIGHT-LINE AND COMPASS CONSTRUCTIONS

Let us study about straight line and compass constructions,
You can draw straight lines, and set the compasses to any radius you like (obviously you can't measure the radius, because you've no markings on your ruler); in particular, if you've managed to mark two points on the (infinite) plane that you're drawing on (normally points are defined when arcs and lines intersect) then you can set the compass to exactly the distance between those points.

example : Draw an equilateral triangle.

Solution :
1. Draw a line, A.
2. Mark two arbitrary points on A, b and c, not coincident. ( The distance bc will be the length of each side of the triangle.)
3. Draw a circle, centre b, radius bc. ( This is two steps rolled into one: 1. Set the compasses to radius bc 2. Draw a circle centred on b )
4. Draw a circle, centre c, radius bc.
5. The two circles will intersect in two points, d and d', one either side of A.
6. Draw the line segments bd and cd. bcd is the equilateral triangle. ( Since lengths bd = bc = cd )

I hope the above explanation was useful.

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