Module 6 (M6) - Geometry and measures - Constructions using a ruler and a compass

Part ofMathsM6: Geometry and measures

Constructions using a ruler and a compass

It may be useful to look at M5 constructions

Constructions are accurate drawings of shapes using a ruler and protractor. In M6 you may be asked to construct using a pair of compasses, a pencil and a ruler

Definitions of perpendicular, bisector and locus

If two lines are drawn at right angles to each other, they are said to be perpendicular.

A line drawn to cut another line or angle in half is a bisector.

The path of a point that moves according to a certain rule is a locus.

The plural of locus is loci.

Practise these constructions until you can do them without looking at the instructions.

How to draw constructions

Perpendicular bisector construction of a line segment

Follow the instructions and draw this perpendicular bisector of a line segment construction.

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Begin by drawing a straight horizontal line.
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Placing your compass at one end of the line, draw an arc - making sure it is over half way across the line.
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Without changing the distance between the pencil and compass point, place your compass at the other end of the line and draw another arc - crossing the first arc in two places.
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The points where the arcs cross (A and B) are exactly the same distance from X and Y.
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Use your ruler to draw a line connecting the points A and B.
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Point M is exactly halfway between X and Y. When drawn correctly, these lines will always be at right angles.

Perpendicular from a point on a line construction

Follow the instructions and draw the perpendicular from a point to a line construction.

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Begin with a straight horizontal line and mark point P over the line.
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Placing your compass on the point, mark the line in two places.
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Label the points A and B.
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Placing your compass on point A, draw an arc - making sure it is over half way across AB, but below the line.
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Without changing the distance between your compass point and pencil, place the compass on point B and do the same - making sure the two arcs cross. Mark this point C. Finally, draw a line connecting points C to the original point P. Line PC is perpendicular to XY.

Draw a perpendicular through a point on a line

Follow the instructions and draw the perpendicular through a point on a line construction

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Draw a straight horizontal line and mark a point, P, anywhere on the line.
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Placing your compass point on P, draw arcs on both sides of P.
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Placing your compass on point A, draw an arc - making sure it is over half way across AB, but above the line.
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Without changing the distance between your compass point and pencil, place the compass on point B and do the same - making sure the two arcs cross.
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Finally, draw a line connecting points C to the original point P. Line CP is perpendicular to XY.

Angle bisector construction

Follow the instructions and draw this angle bisector construction.

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Begin by drawing two lines, meeting at a point. Mark this point V.
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Place your compass on the point where the lines meet, draw an arc that crosses both lines.
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Label the points A and B.
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Place your compass on the point A, draw an arc towards the middle.
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Without changing the distance between your compass point and your pencil, place the compass on point B and draw an arc towards the middle - making sure that the two arcs cross. Mark this point C.
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Finally, using a ruler connect point C to point V. Line VC bisects the angle AVB.

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