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

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We started drawing some quadrilaterals - can you complete them?

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

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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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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?

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

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How many questions do you need to identify my quadrilateral?

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

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

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

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