Constructing Shapes

You need to be able to use these construction methods along with a protractor to draw triangles or other shapes with specific angles or side lengths.  For instance, say you’re asked to draw a triangle which has the following side lengths – 4 cm, 7 cm and 9 cm.  What you can do is first draw the longest side as a horizontal line (note these lines won’t actually be 9 cm long if you measure them with a ruler, if you want to try these instructions out do them on a separate piece of paper):

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Then what you need to do is set your compass radius so that it is the length of one of the other sides, say the 7 cm side.  Put the tip at one end of the 9 cm line and draw an arc above it, like this:

Then, for the other end of the 9 cm line, set the compass to have a radius of 4 cm, which is the length of the other remaining side.  Draw another arc, which should intersect nicely with the first arc:

The intersection point of the two arcs is a point that is exactly 7 cm from one end of the 9 cm line, and exactly 4 cm from the other end of the 9 cm line. This is exactly what we want for the third corner of our triangle.  So all we need to do is draw a straight line from each end of the 9 cm line to the intersection point:

A good check is to measure the lengths of the two new lines just to check that they are as long as they should be.

You can also draw a triangle easily in the following two situations:

·         You’re given the length of two sides and the angle between those two sides

·         You’re given two angles and the side between these two angles

In the first case, you’ve given something like this:

All you need to do is draw a straight line to make up the third side of the triangle.  If the question’s a little more difficult, they might give you the side lengths and the angle separately, like this:

In this case, what you can do is first set the compass radius to the length of the shorter line.  Then, put the compass tip on the angle point, and draw an arc roughly in line with one of the dotted angle lines:

Doing the same for the other side length, using the other dotted angle line, you get:

Then all you’ve got to do is extend the dotted angle lines out until they intersect the arcs, and you’ve got the other two corners of your triangle.  Then just join all the corners together with straight lines:

If you’re given two angles and the side length between those angles, all you’ve got to do is draw two new sides starting at each end of the side you’re given, heading out at the appropriate angle, until they intersect.  So if you’re given this:

All you do is just extend the dotted lines out until they meet, and you’ve got your triangle: