List

Angles, polygons and geometrical proof: Age 11-14

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

Estimating angles
game
Favourite

Estimating angles

Age
7 to 14
Challenge level
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How good are you at estimating angles?

Guess \my Quad
problem

Guess my quad

Age
11 to 14
Challenge level
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How many questions do you need to identify my quadrilateral?

Polygon Rings
problem

Polygon rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

Completing Quadrilaterals
problem

Completing quadrilaterals

Age
11 to 14
Challenge level
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We started drawing some quadrilaterals - can you complete them?

Polygon Pictures
problem

Polygon pictures

Age
11 to 14
Challenge level
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Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Parallelogram It
problem

Parallelogram it

Age
11 to 16
Challenge level
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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 parallelogram.

Quadrilaterals game
game
Favourite

Quadrilaterals game

Age
11 to 14
Challenge level
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A game for 2 or more people, based on the traditional card game Rummy.
Tilted Squares
problem

Tilted squares

Age
11 to 14
Challenge level
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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Square It
problem

Square it

Age
11 to 16
Challenge level
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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.

Triangles in circles
problem

Triangles in circles

Age
11 to 14
Challenge level
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Can you find triangles on a 9-point circle? Can you work out their angles?

Semi-regular Tessellations
problem

Semi-regular tessellations

Age
11 to 16
Challenge level
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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?

Cyclic Quadrilaterals
problem

Cyclic quadrilaterals

Age
11 to 16
Challenge level
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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Hidden Squares
problem

Hidden squares

Age
11 to 14
Challenge level
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Can you find the squares hidden on these coordinate grids?

Quadrilaterals in a Square
problem

Quadrilaterals in a square

Age
11 to 14
Challenge level
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What's special about the area of quadrilaterals drawn in a square?

Star Polygons
problem

Star polygons

Age
11 to 14
Challenge level
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Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Rhombus It
problem

Rhombus it

Age
11 to 16
Challenge level
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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 rhombus.

Square coordinates
problem

Square coordinates

Age
11 to 14
Challenge level
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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?

Subtended angles
problem

Subtended angles

Age
11 to 14
Challenge level
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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?

Right angles
problem

Right angles

Age
11 to 14
Challenge level
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Shapely pairs
problem

Shapely pairs

Age
11 to 14
Challenge level
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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...

Property chart
problem

Property chart

Age
11 to 14
Challenge level
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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?

Pythagoras Proofs
problem

Pythagoras proofs

Age
11 to 16
Challenge level
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Can you make sense of these three proofs of Pythagoras' Theorem?

Opposite vertices
problem

Opposite vertices

Age
11 to 14
Challenge level
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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Which solids can we make?
problem

Which solids can we make?

Age
11 to 14
Challenge level
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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?

Of all the areas
problem

Of all the areas

Age
14 to 16
Challenge level
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Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?



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Angles, Polygons Stage 3 STEM footer
 

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