Similarity and congruence

problem
Partly circles

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

7 to 11

Challenge level

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

Age

5 to 7

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Wedge on wedge

Age

14 to 16

Challenge level

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?
problem
All about ratios

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

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.