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.

See the TETRA SQUARE poster.

This activity is adapted from the NRICH task Tetra Square with permission of the University of Cambridge. All rights reserved.