Given: Two right triangles are given such that-
[tex]\Delta LMO\cong\Delta LNO[/tex]
Required: To determine the missing information to prove the given statement.
Explanation: The HL theorem states that two right triangles are congruent if their hypotenuse and a leg of one triangle are equal to the hypotenuse and a leg of another triangle.
We are given two right triangles whose hypotenuse is their common side.
Hence hypotenuse of both triangles LMO and LNO are equal to each other i.e.,
[tex]LO=LO\text{ }(\text{Common})[/tex]
Now we need one leg of both triangles which are congruent to each other.
As there are two legs in both triangles which can be used to prove the congruency-
[tex]\begin{gathered} OM=ON\text{ or} \\ LM=LN \end{gathered}[/tex]
Any one of the legs shown above can be used to prove the congruency of the triangles by HL theoe
