Construction using compasses works because all the points

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. . A Point B is exactly the same distance away from the centre of the circle as Point A. x. B Equidistant means: The same distance from So: A and B are equidistant from X an Arc is a part of a circle circumference. So: the circumference segment AB is an arc.

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

Construction using compasses Constructing the bisector of a straight line segment. Bisector means cutting the straight line in two section equally sized sections Keeping same Place Set your thethe point compasses of radius, your to a put radius Draw the line segment AB C the point of at your compasses that is more than point half A and draw making sure that itthe has on B above and 2 below more arcs length the andline segment the twoofdraw very distinct endsto cross the two already drawn line segment X A B at points C and D 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

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 of of thethe compasses on Setthe thepoint radius compasses Xto&about Y in turn half and waydraw alongarcs the that lines intersect at Z Put the point of the compasses on B X point A and draw two arcs to cut Z AB and AC A Y C This identifies two points X & Y equidistant A N. B youfrom mustpoint always Show the construction arcs 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

Construction using compasses Constructing a perpendicular from a point P on a line segment. C A B P Put ofof the compasses Set the radius the compassesontotobe Join CP. point CP is the perpendicular thelarger original P, draw cut the line with 2 aarcs 90 oto angle at Pline segment at A and B Put Notice the point A and B in. Aturn drawbeen arcs thatononce points andand B have thatfound intersect C the at construction is identical to finding the perpendicular bisector of the line. Why?

Construction using compasses Constructing a perpendicular from a point P onto a line segment. Now construct thethe perpendicular With the point of compasses on P, bisector asarcs before draw two that intersect the line P at A and B 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 90 o angle at P

Construction using compasses Constructing an angle of 60 o. R P 60 o Because the same radius was used Join the points together P, R and Q are all equidistant What shape do you draw? from each other. Equilateral triangle The internal angles in an equilateral triangle are all 60 o Q 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