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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.

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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?

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

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?

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

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

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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...

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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?

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

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

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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?

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

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How many questions do you need to identify my quadrilateral?

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We started drawing some quadrilaterals - can you complete them?

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

Challenge Level

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

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

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Can you find the squares hidden on these coordinate grids?

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

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

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

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

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

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

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.

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.