This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
Cyclic quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Same length
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Making sixty
Why does this fold create an angle of sixty degrees?
Circles in quadrilaterals
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Isosceles seven
Is it possible to find the angles in this rather special isosceles triangle?
Triangle midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Two ladders
Two ladders are propped up against facing walls. At what height do the ladders cross?
Quad in quad
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Sitting pretty
Trapezium four
Nicely similar
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?
Kite in a square
The square under the hypotenuse
Napkin
Angle trisection
Squirty
Partly circles
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.