Angles, Polygons and Geometrical Proof - Stage 3

Square It

Age 11 to 16
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 square.

Square Coordinates

Age 11 to 14
Challenge Level

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

Age 11 to 14
Challenge Level

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

Subtended Angles

Age 11 to 14
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?

Right Angles

Age 11 to 14
Challenge Level

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

Quadrilaterals Game

Age 11 to 14
Challenge Level

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

Shapely Pairs

Age 11 to 14
Challenge Level

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

Age 11 to 14
Challenge Level

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

Age 11 to 16
Challenge Level

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

Cyclic Quadrilaterals

Age 11 to 16
Challenge Level

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

Which Solids Can We Make?

Age 11 to 14
Challenge Level

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

Age 11 to 14
Challenge Level

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

Guess my Quad

Age 11 to 14
Challenge Level

How many questions do you need to identify my quadrilateral?

Completing Quadrilaterals

Age 11 to 14
Challenge Level

We started drawing some quadrilaterals - can you complete them?

Angles, Polygons and Geometrical Proof Short Problems

Age 11 to 16

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

Of All the Areas

Age 14 to 16
Challenge Level

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

Estimating Angles

Age 7 to 14
Challenge Level

How good are you at estimating angles?

Tilted Squares

Age 11 to 14
Challenge Level

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

Hidden Squares

Age 11 to 14
Challenge Level

Can you find the squares hidden on these coordinate grids?

Quadrilaterals in a Square

Age 11 to 14
Challenge Level

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

Polygon Rings

Age 11 to 14
Challenge Level

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

Star Polygons

Age 11 to 14
Challenge Level

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

Polygon Pictures

Age 11 to 14
Challenge Level

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

An Equilateral Triangular Problem

Age 11 to 14
Challenge Level

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

Angles Inside

Age 11 to 14
Challenge Level

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