Construction using compasses

1. Construction using compasses Construction using compasses works because all the points on the radius of a circle are exactly the same distance away from the centre of the circle. Point B is exactly the same distance away from the centre of the circle as Point A. . A x . B an Arc is a part of a circle circumference. Equidistant means: The same distance from So: the circumference segment AB is an arc. So: A and B are equidistant from X

2. Construction using compasses This means that for 2 circles that overlap – if the circles are the same size, the points where they cross are the equidistant from the circle centres Point A is equidistant from the centres of both circles A . x x . B Point B is also equidistant from the centres of both circles

3. Construction using compasses Constructing the bisector of a straight line segment. Bisector Bi sector means cutting the straight line in two equally sized sections two section Keeping the same radius, put the point of your compasses on B and draw 2 more arcs to cross the two already drawn at points C and D Place the point of your compasses at point A and draw arcs above and below the line segment Set your compasses to a radius that is more than half the length of the line segment Draw the line segment AB making sure that it has two very distinct ends C X A B N.B you must always Show the construction arcs D Now draw a straight line from C to D. The line crosses AB at X which is the mid-point of AB The line CD is the perpendicular bisector of AB

4. Construction using compasses Constructing the bisector of an angle. Bisect angle BAC N.B. The vertex of the angle is always the middle letter Put the point of the compasses on X & Y in turn and draw arcs that intersect at Z Set the radius of the compasses to about half way along the lines Put the point of the compasses on point A and draw two arcs to cut AB and AC B X Z A This identifies two points X & Y equidistant from point A N.B you must always Show the construction arcs Y C Draw a line from A to Z – this is the bisector of the angle This works for any kind of angle acute, obtuse or reflex

5. Construction using compasses Constructing a perpendicular from a point P on a line segment. C A B P Put the point of the compasses on P, draw 2 arcs to cut the line segment at A and B Set the radius of the compasses to be larger Join CP. CP is the perpendicular to the original line with a 90o angle at P Put the point on A and B in turn and draw arcs that intersect at C Notice that once points A and B have been found the construction is identical to finding the perpendicular bisector of the line. Why?

6. Construction using compasses Constructing a perpendicular from a point P onto a line segment. Now construct the perpendicular bisector as before With the point of the compasses on P, draw two arcs that intersect the line at A and B P B A Put the point on A and B in turn and draw arcs that intersect at C C Join CP. CP is the perpendicular to the original line with a 90o angle at P

7. Construction using compasses Because the same radius was used P, R and Q are all equidistant from each other. Join the points together What shape do you draw? Constructing an angle of 60o. R Equilateral triangle The internal angles in an equilateral triangle are all 60o 60o Q P Draw a large arc that intersects the line at Q Keeping the radius the same and draw an arc from Q that intersects at P and crosses the other arc