Symmetry

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?

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?

What is the missing symbol? Can you decode this in a similar way?

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.

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

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

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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

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

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