Question

which triangle congruence theorem/postulate can be used to prove $\triangle jkn \cong \triangle lkn$.
\bigcirc\\ leg-leg
\bigcirc\\ side-angle-side
\bigcirc\\ side-side-angle

Explanation:

From the diagram, ∠JKN and ∠LKN are right angles (marked with a square), so △JK N and △LK N are right triangles. They share the leg KN, and if JK ≅ LK (implied by the congruent triangle setup), the Leg-Leg (LL) theorem (for right triangles: if two legs of one right triangle are congruent to two legs of another right triangle, the triangles are congruent) applies. The other options don’t fit: SAS needs an included angle, SSA is not a valid congruence postulate. Thus, Leg-Leg is correct.

Answer:

Leg-Leg