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. 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

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 14 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?

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 11 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?

Triangle in the Corner

Age 11 to 14 Short Challenge Level:

A triangle is shaded within a regular hexagon. Can you find its area?

Funky Hexagon

Age 11 to 14 Short Challenge Level:

Can you find the value of x in this diagram?

Perimeter in a Hexagon

Age 11 to 14 Short Challenge Level:

Can you find the perimeter of this triangle inscribed in a hexagon?

Tricky Tessellations

Age 11 to 14 Short Challenge Level:

Can you work out the fraction of the tiles that are painted black in this pattern?

Descending Angles

Age 11 to 14 Short Challenge Level:

Given four of the angles in two triangles, can you find the smallest angle overall?

Clock Face Angles

Age 11 to 14 Short Challenge Level:

The time is 20:14. What is the smaller angle between the hour hand and the minute hand on an accurate analogue clock?

Overlapping Beer Mats

Age 11 to 14 Short Challenge Level:

Can you find the area of the overlap when these two beer mats are placed on top of each other?

Clock Angle

Age 11 to 14 Short Challenge Level:

What is the angle between the the hands of a clock at 8:24?

Two Triangles

Age 11 to 14 Short Challenge Level:

Prove that the angle marked $a$ is half the size of the angle marked $b$.

Inner Rectangle

Age 11 to 14 Short Challenge Level:

If the shape on the inside is a rectangle, what can you say about the shape on the outside?

No Rights

Age 11 to 14 Short Challenge Level:

Prove that the angle bisectors of a triangle can never meet at right angles.

Perimeter Puzzle

Age 11 to 14 Short Challenge Level:

If four copies of this triangle are joined together to form a parallelogram, what is the largest possible perimeter of the parallelogram?

Diagonal Side

Age 11 to 14 Short Challenge Level:

Can you work out the area of a square drawn on a diagonal?

Add All the Angles

Age 11 to 14 Short Challenge Level:

Find the sum of all of the angles denoted by letters in this diagram

Fraction of a Square

Age 11 to 14 Short Challenge Level:

What fraction of this square is shaded?