home Interactive Shape Think!
a1 a2 a3 a4
b1 b2 b3 b4
b1 c2 b3 b4
ks1 ks3 & ks4 Foundation
ks2 ks4 Higher
ks4 Higher Squares are constructed on the four sides of a parallelogram. Their centres form a square. Can you prove it?

This is known as Thébault's theorem, first published in 1937. This diagram illustrates the proof. Can you see it?
Please enable Java for an interactive construction (with Cinderella).