What additional information do you need to prove that ∆LMX ≅ ∆LOX by the HL Theorem?

LM = LO

Explanation: In order to use the HL Theorem the triangles included must be right triangles and in this case they must have a congruent hypotenuse and in order for that, LM must be congruent to LO.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.