Isosceles right triangle 45°-45°-90°

The isosceles right triangle is half of a square cut along the diagonal: the two legs are equal and the hypotenuse is the leg times $\sqrt{2}$.

Theorem — 45°-45°-90° triangle

In an isosceles right triangle (angles $45°$, $45°$, $90°$) the two legs are congruent and the hypotenuse equals a leg times $\sqrt{2}$: $\text{se } a = b \quad\implies\quad c = a\sqrt{2}.$

The two congruent legs $a$ and the hypotenuse $a\sqrt{2}$.

Example — Diagonal of the square

The diagonal of a square of side $\ell$ is $d = \ell\sqrt{2}$; conversely, given a square with diagonal $d$, the side is $\ell = \dfrac{d}{\sqrt{2}} = \dfrac{d\sqrt{2}}{2}$.

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Topics: Euclidean circle
Concepts: Right triangle
Skills: Calculating · Using formulae