Friday, 6 April 2012

As if by magic, a right angle appeared...

Year 5 looked at a certain kind of triangle. It's one inside a circle where the long side of the triangle is the diameter of the circle. The opposite corner is on the circle too.

At first we looked at these triangles on a big scale. The school pitch, like every football pitch, has a very convenient circle, with a straight line right through its middle. If that line is the long side of a triangle, what angle would the opposite corner have?

Next we used a pair of compasses and a ruler to recreate the situation:

We've also started using GeoGebra  in Year 5. It's great for showing how the angle is always 90°:

GeoGebra Dynamic Worksheet
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

I didn't take it on to this with Year 5, but there is a fairly simple proof that this will be always the case...