Three By One

This rectangle measures three units by one unit.

The diagram shows three angles a, b and c.

How many ways can you prove that a + b = c?

What other interesting properties can you find?

When this activity was originally published on NRICH, two boys from Madras School in St Andrew’s, Scotland sent in 8 different solutions to this problem using 8 different methods including trigonometry, Euclidean geometry,  analytic geometry, vectors, matrices and complex numbers.

This activity is adapted from the NRICH task Three by One with permission of the University of Cambridge. All rights reserved.

AIMSSEC Teacher Notes THREE BY ONE