Question

9. What additional information do you need to prove that LMO LNO by the HL Theorem?LMON

Answer 1

Given: Two right triangles are given such that-

$\Delta LMO\cong\Delta LNO$

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.,

$LO=LO\text{ }(\text{Common})$

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-

$\begin{gathered} OM=ON\text{ or} \\ LM=LN \end{gathered}$

Any one of the legs shown above can be used to prove the congruency of the triangles by HL theoe