Question

9. What additional information do you need to prove that

Answer 1

$OM=ON$

Explanation

The Hypotenuse leg theorem states that if the hypotenuse and leg of a triangle are congruent to the hypotenuse and leg of another rigth triangle then the two triangles are congruent

therefore, to prove the triangles are congruent we need to know that

$\begin{gathered} hypotenuse1=\text{ hypotenuse2} \\ LM=LO \end{gathered}$

also, the legs must be congruent, so

$OM=ON$

therefore, the answer is

$OM=ON$

I hope this helps you