Year 10 Reasoning, convincing and proving

Can you find the values at the vertices when you know the values on the edges?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Why does this fold create an angle of sixty degrees?

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

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Have you ever wondered what it would be like to race against Usain Bolt?

Is it possible to find the angles in this rather special isosceles triangle?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?