Definition: The HL criterion states that two right triangles are congruent if their hypotenuses are congruent and one pair of legs is congruent.
When does HL apply?
Only to right triangles. You need the hypotenuse of each triangle, the side opposite the right angle, and one leg of each. The right angles themselves supply the third part automatically.
Why does it work?
The Pythagorean theorem gives the remaining leg: if the hypotenuse and one leg are known, the other leg is determined. So the two triangles match in all three sides, which is SSS in disguise.
Example. Right triangle ABC has hypotenuse AB = 17 and leg BC = 8. Right triangle DEF has hypotenuse DE = 17 and leg EF = 8. The third legs satisfy AC2 = 289 – 64 = 225, so AC = 15, and likewise DF = 15. The triangles are congruent by HL.
What mistake is typical?
Using HL when the triangle is not known to be right, or matching a leg with a hypotenuse. The side that is equal in length must have the same role in both triangles. HL is a shortcut that avoids the problem with SSA, because it works only in the right-triangle case.