HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called 'legs', or 'base' and 'height'.
It means we have two right-angled triangles with
the same length of hypotenuse
the same length for one of the other two legs
Since ∠ LMN and ∠KMN are right angle , the hypotenuse LN and and one leg LN of one right-angled triangle LMN are equal to the corresponding hypotenuse KN and leg MN of another right-angled triangle MKN, hence the two triangles are congruent.
If we want to prove that two right triangles are congruent by knowing that the corresponding hypotenuses and one leg are congruent, we begin as follows:
Since two legs are congruent and we know this by the hash marks, then the triangle ΔLKN is isosceles.
By definition LN ≅ NK
If ∠LMN is a right angle, then MN is the altitude of triangle ΔLKN
Also MN is the bisector of LK, so KM ≅ ML
So we have two right triangles ΔLMN and ΔKM having the same lengths of corresponding sides
