Angles, Polygons and Geometrical Proof: Age 11-14

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

Can you find the squares hidden on these coordinate grids?

How many questions do you need to identify my quadrilateral?

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

We started drawing some quadrilaterals - can you complete them?

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

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

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?

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?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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...

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?

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

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

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

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?

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.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

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.

Can you make sense of these three proofs of Pythagoras' Theorem?

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.