You may also like

problem icon

Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

problem icon

Proofs with Pictures

Some diagrammatic 'proofs' of algebraic identities and inequalities.

problem icon

For What?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

Cosines Rule

Age 14 to 16 Challenge Level:

(a) Prove that a triangle with sides $3$, $7$, $8$ contains a $60$ degree angle.

(b) Three points $A$, $B$ and $C$ lie in this order on a line, and $P$ is any point in the plane. Use the Cosine Rule to prove that:

\[{AP^2\over AB.AC}+{CP^2\over CA.CB} = 1 + {PB^2\over BA.BC}.\]

Triangle.