Constructions

Slideshow 39, MathematicsMr Richard SasakiRoom 307

OBJECTIVES

• Learn the tools necessary for constructions

• Learn how to construct a regular hexagon

• Learn how to construct triangles

THE CIRCLE

Let’s review circle properties!

Centre (origin)

Radius

Tangent

THE CIRCLEDiameter

Chord

Sector

Radii (plural of radius)

Centre (origin)Central

angleArc length

CONSTRUCTIONS

Constructing in mathematics is drawing accurately with a pencil, ruler and compass. (A protractor is not allowed.)Constructing straight line segments is very easy (of course, just use a ruler!) but other shapes may need a little more thought.

CIRCLESPeople consider a compass as a tool to draw circles. It’s perfect for this!

Radius

We need to measure the radius with the ruler. Try Questions 1 - 3!

A REGULAR HEXAGONTo draw a regular hexagon where say, each edge is 5cm, we first draw a circle with radius 5cm.

5 cm

Then, keeping the compass at 5cm, we place the point of the compass on the circle’s edge and draw a short arc across over the edge.

A REGULAR HEXAGONNext, keeping the compass at 5cm, we place the compass point on the arc and make another arc on the circle’s edge. We do this all the way around.

A REGULAR HEXAGONFinally we join the points marked on the circle with straight lines with our ruler and they should form a regular hexagon.

Finally rub out the circle and the extra marks! Try a 4cm one too!

A TRIANGLEIf we are given the lengths of every edge, we can draw a triangle with a compass.

Let’s try a 3cm, 4cm, 5cm triangle.

First with a ruler, draw a 5cm edge.

A TRIANGLENext, from either side (let’s say left), draw an arc 4cm from the left point and estimate where the arcs will cross. Usually it will be above and around the centre of the edge drawn.

Next from the right, measure 3cm with an arc. Make sure the arcs cross.

Finally, join the intersection to both points on the line segment.Try the second

part!