shape & space : constructions
 

line bisector

 

 

 

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

construction#1

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

 

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Perpendicular from a point to a line

 

construction #2

 

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

 

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Bisection of an angle

construction #3

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

 

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

 

construction #4

 

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

 

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Construction of a triangle(sides different)

 

construction #5

 

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

 

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