Tetrasquare

ABCD is a regular tetrahedron and the points P, Q, R and S

are the midpoints of the edges AB, BD, CD and CA.

Prove that PQRS is a square.

What does this tell you about the opposite edges of the tetrahedron?

To help with visualising the problem you might like to make a tetrahedron using six sticks made from paper rolled around pieces of string that you tie together at the vertices.

See the Notes for Teachers.