Symmetry

problem
Sliced

Age

14 to 16

Challenge level

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?
problem
Symmetrical semaphore

Age

7 to 11

Challenge level

Someone at the top of a hill sends a message in semaphore to a friend in the valley. A person in the valley behind also sees the same message. What is it?
problem
Hidden meaning

Age

7 to 11

Challenge level

What is the missing symbol? Can you decode this in a similar way?
problem
Two triangles in a square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
problem
Symmetry challenge

Age

7 to 11

Challenge level

How many symmetric designs can you make on this grid? Can you find them all?
problem
Shady symmetry

Age

11 to 14

Challenge level

How many different symmetrical shapes can you make by shading triangles or squares?
problem
Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?
problem
Classifying solids using angle deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem
A Cartesian puzzle

Age

7 to 11

Challenge level

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
problem
Overlap

Age

14 to 16

Challenge level

A red square and a blue square overlap. Is the area of the overlap always the same?