Similarity and congruence

What is the same and what is different about these circle questions? What connections can you make?

Weekly Problem 4 - 2008
In the figure given in the problem, calculate the length of an edge.

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Can you sort these triangles into three different families and explain how you did it?

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?

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.