Hypotenuse-Leg theorem

The Hypotenuse-Leg (HL) theorem states that if two right triangles have the same length of hypotenuse (the longest side) and one pair of corresponding legs (the shorter sides) are equal in length, then the triangles are congruent—meaning they are identical in shape and size. This theorem is useful for proving that two right triangles are exactly the same without needing to compare all sides and angles. Essentially, knowing one pair of legs and the hypotenuse are equal is enough to confirm the entire triangles match perfectly.