Question

what congruence criteria is needed to prove the triangles are congruent by hl?

select one:
a. \\(\angle n \cong \angle k\\)
b. \\(\overline{jk} \cong \overline{mn}\\)
c. \\(\angle j \cong \angle m\\)
d. \\(\overline{nl} \cong \overline{kl}\\)

Explanation:

⚡ Using what you learned: congruence criteria for triangles (sss, sas, asa, aas, hl)

Step 1: Identify the given components

From the diagram, we have:

• A right angle at \( L \), which means \(\angle NLM\) is a right angle. Since \(\angle JLK\) and \(\angle NLM\) are vertical angles, both \(\triangle JLK\) and \(\triangle NLM\) are right triangles.
• Congruent segments marked with double tick marks:

$$ JL \cong ML $$

In these right triangles, \(JL\) and \(ML\) are legs.

Step 2: Apply the HL congruence criteria

The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

• We already have a congruent Leg: \(JL \cong ML\).
• We need the Hypotenuses of both right triangles to be congruent.
• The hypotenuse is the side opposite the right angle:
• In right \(\triangle JLK\), the hypotenuse is \(JK\).
• In right \(\triangle NLM\), the hypotenuse is \(MN\).

Therefore, the additional information needed is:

$$ \overline{JK} \cong \overline{MN} $$

Answer:

b. \(\overline{JK} \cong \overline{MN}\)