Angles and Polygons

Tet-trouble

Stage: 4 Challenge Level: Challenge Level:1

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Square It

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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.

Square Coordinates

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Triangles in Circles

Stage: 3 Challenge Level: Challenge Level:1

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Subtended Angles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Quadrilaterals Game

Stage: 3 Challenge Level: Challenge Level:1

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and two properties of the shape.

Shapely Pairs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Semi-regular Tessellations

Stage: 3 Challenge Level: Challenge Level:1

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

Eight Hidden Squares

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Cyclic Quadrilaterals

Stage: 3 Challenge Level: Challenge Level:1

What can you say about the angles on opposite vertices of any cyclic quadrilateral? Working on the building blocks will give you insights that may help you to explain what is special about them.

Which Solids Can We Make?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Opposite Vertices

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Angles and Polygons - Short Problems

Stage: 3 Challenge Level: Challenge Level:1

A collection of short Stage 3 problems on Angles and Polygons.