Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you find all the different triangles on these peg boards, and
find their angles?
The large rectangle is divided into a series of smaller
quadrilaterals and triangles. Can you untangle what fractional part
is represented by each of the ten numbered shapes?
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?
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...
How many triangles can you make on the 3 by 3 pegboard?
The graph below is an oblique coordinate system based on 60 degree
angles. It was drawn on isometric paper. What kinds of triangles do
these points form?
How many different triangles can you make on a circular pegboard
that has nine pegs?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
ABC is an equilateral triangle and P is a point in the interior of
the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP
must be less than 10 cm.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
A group activity using visualisation of squares and triangles.
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
What shapes can you make by folding an A4 piece of paper?
Draw all the possible distinct triangles on a 4 x 4 dotty grid.
Convince me that you have all possible triangles.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
I cut this square into two different shapes. What can you say about
the relationship between them?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
You have pitched your tent (the red triangle) on an island. Can you
move it to the position shown by the purple triangle making sure
you obey the rules?
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
Determine the total shaded area of the 'kissing triangles'.
If you know the sizes of the angles marked with coloured dots in
this diagram which angles can you find by calculation?
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
What is the total area of the first two triangles as a fraction of
the original A4 rectangle? What is the total area of the first
three triangles as a fraction of the original A4 rectangle? If. . . .
Explain how the thirteen pieces making up the regular hexagon shown
in the diagram can be re-assembled to form three smaller regular
hexagons congruent to each other.
Can you describe what happens in this film?