Question

mark any congruent parts on the triangles that can be proved. what additional piece of information is required to prove the triangles congruent by hl ≅?

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) Congruence Theorem

The HL theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.
In the given figure, we know that \(MP\perp NL\), so \(\angle MPN=\angle MPL = 90^{\circ}\). The hypotenuse is \(MN\) and \(ML\) (if we consider \(\triangle MPN\) and \(\triangle MPL\)), and the leg is \(MP\) (common side).

Step2: Identify the required congruent parts

For \(\triangle MPN\) and \(\triangle MPL\) to be congruent by HL:

• We already have \(\angle MPN=\angle MPL = 90^{\circ}\) (right angles) and \(MP = MP\) (common leg).
• We need to mark that \(MN=ML\) (hypotenuses of the right - triangles \(\triangle MPN\) and \(\triangle MPL\))

Answer:

\(MN = ML\)