Coursework Notes - Shape & Space

Constructions

 line bisector point to line bisect angle triangle

The perpendicular bisector of a line(also line equidistant from two points)

 set the radius of your compass to more than than half the length of XY(but less than XY)   with centre X, draw an arc above and below the line XY   with centre Y, draw an arc above and below the line XY intersecting the arcs from X   the arcs intersect at points W and Z respectively above and below the line XY   join the points W and Z   the line WZ is the perpendicular bisector of XY

Perpendicular from a point to a line

 set the radius of your compass so that an arc with centre P cuts the line at two points   name these points of intersection X and Y   with the radius greater than half XY and centre X draw an arc below the line XY   repeat with centre Y   where the arcs intersect call point Z   the line joining Z to P is the perpendicular bisector of the line XY   where this line meets XY call point W   PW is the perpendicular from the point P to the line XY

Bisection of an angle

 with centre O draw arcs to cut the arms of the angle at X and Y   using the same radius, from point X draw an arc between the arms of the angle   repeat at point Y   the two arcs intersect at point P   draw a line between P and O   PO is the bisector of the angle XOY

Construction of a 60 deg. angle (also of an equilateral triangle)

 draw a line XY   with centre X and radius the length of the line, draw an arc above the line   repeat from centre Y   the point Z is where the arcs intersect   join XZ   join YZ   angle ZXY is a 60 deg. angle

Construction of a triangle(sides different)

 draw a line XY of given length, as the base to the triangle   with centre X and radius the length of the second side of the triangle, draw an arc above the line   with centre Y and radius the length of the third side of the triangle, draw an arc above the line   the point Z is where the arcs intersect   join XZ   join YZ

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