Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Square Coordinates
Age 11 to 14
Challenge Level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Triangles in Circles
Age 11 to 14
Challenge Level
Can you find triangles on a 9-point circle? Can you work out their angles?
Subtended Angles
Age 11 to 14
Challenge Level
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Right Angles
Age 11 to 14
Challenge Level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Quadrilaterals Game
Age 11 to 14
Challenge Level
A game for 2 or more people, based on the traditional card game Rummy.
Shapely Pairs
Age 11 to 14
Challenge Level
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
Property Chart
Age 11 to 14
Challenge Level
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Cyclic Quadrilaterals
Age 11 to 16
Challenge Level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Opposite Vertices
Age 11 to 14
Challenge Level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Guess my Quad
Age 11 to 14
Challenge Level
How many questions do you need to identify my quadrilateral?
Completing Quadrilaterals
Age 11 to 14
Challenge Level
We started drawing some quadrilaterals - can you complete them?
Angles, Polygons and Geometrical Proof Short Problems
Age 11 to 16
A collection of short problems on Angles, Polygons and Geometrical Proof.
Of All the Areas
Age 14 to 16
Challenge Level
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Hidden Squares
Age 11 to 14
Challenge Level
Can you find the squares hidden on these coordinate grids?
Quadrilaterals in a Square
Age 11 to 14
Challenge Level
What's special about the area of quadrilaterals drawn in a square?
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
Star Polygons
Age 11 to 14
Challenge Level
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
Polygon Pictures
Age 11 to 14
Challenge Level
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
An Equilateral Triangular Problem
Age 11 to 14
Challenge Level
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
Angles Inside
Age 11 to 14
Challenge Level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
Parallelogram It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
Rhombus It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
NRICH is part of the family of activities in the Millennium Mathematics Project.