Angles, Polygons and Geometrical Proof (age 11-14)
Polygon Rings
Join pentagons together edge to edge. Will they form a ring?
Completing Quadrilaterals
We started drawing some quadrilaterals - can you complete them?
Quadrilaterals Game
A game for 2 or more people, based on the traditional card game Rummy.
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Hidden Squares
Can you find the squares hidden on these coordinate grids?
Polygon Pictures
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
An Equilateral Triangular Problem
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
Angles Inside
Draw some angles inside a rectangle. What do you notice? Can you prove it?
Triangles in Circles
Can you find triangles on a 9-point circle? Can you work out their angles?
Guess my Quad
How many questions do you need to identify my quadrilateral?
Subtended Angles
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
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Opposite Vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Star Polygons
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
Property Chart
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?
Square Coordinates
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?
Quadrilaterals in a Square
What's special about the area of quadrilaterals drawn in a square?
Which Solids Can We Make?
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?
Shapely Pairs
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...
Square It
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
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Cyclic Quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Of All the Areas
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Angles, Polygons and Geometrical Proof Short Problems
A collection of short problems on Angles, Polygons and Geometrical Proof.
Parallelogram It
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.
Rhombus It
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.
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.