Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Angles, Polygons and Geometrical Proof (age 11-14)

### Polygon Rings

### Completing Quadrilaterals

### Quadrilaterals Game

### Tilted Squares

### Hidden Squares

### Polygon Pictures

### An Equilateral Triangular Problem

### Angles Inside

### Triangles in Circles

### Guess my Quad

### Subtended Angles

### Right Angles

### Opposite Vertices

### Star Polygons

### Property Chart

### Square Coordinates

### Quadrilaterals in a Square

### Which Solids Can We Make?

### Shapely PairsLive

### Square It

### Semi-regular Tessellations

### Cyclic Quadrilaterals

### Of All the Areas

### Angles, Polygons and Geometrical Proof Short Problems

### Parallelogram It

### Rhombus It

Y*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*

Or search by topic

Age 11 to 14

Challenge Level

Join pentagons together edge to edge. Will they form a ring?

Age 11 to 14

Challenge Level

We started drawing some quadrilaterals - can you complete them?

Age 11 to 14

Challenge Level

A game for 2 or more people, based on the traditional card game Rummy.

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?

Age 11 to 14

Challenge Level

Can you find the squares hidden on these coordinate grids?

Age 11 to 14

Challenge Level

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Age 11 to 14

Challenge Level

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

Age 11 to 14

Challenge Level

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Age 11 to 14

Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

Age 11 to 14

Challenge Level

How many questions do you need to identify my quadrilateral?

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?

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?

Age 11 to 14

Challenge Level

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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?

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?

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?

Age 11 to 14

Challenge Level

What's special about the area of quadrilaterals drawn in a square?

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?

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...

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.

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?

Age 11 to 16

Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Age 14 to 16

Challenge Level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Age 11 to 16

A collection of short problems on Angles, Polygons and Geometrical Proof.

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.

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.

Y