Constructions

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.