A quadrilateral PQRS has vertices P(3, 0), Q(6, 4), R(11, 4) and S(8, 0). What is the most precise description of PQRS?

PQ = $\sqrt{3^2+4^2}=5$, QR = $\sqrt{5^2+0^2}=5$, RS = $\sqrt{(8-11{)}^2+(0-4{)}^2}=5$, SP = $\sqrt{(3-8{)}^2+0^2}=5$ — all four sides equal, so PQRS is at least a rhombus. Now the diagonals: PR = $\sqrt{8^2+4^2}=\sqrt{80}$ and QS = $\sqrt{2^2+(-4{)}^2}=\sqrt{20}$. They are unequal, so there are no right angles and PQRS is not a square or a rectangle. Jumping from 'all sides equal' straight to 'square' is the standard mistake — the diagonal test is what separates the two.