__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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