Question

which triangle congruence theorem/postulate can be used to prove △jkn ≅ △lkn.
○ leg-leg
○ side-angle-side
○ side-side-angle
○ hypotenuse-leg

Explanation:

Step1: Analyze the triangle

We have two right triangles $\triangle JKN$ and $\triangle LKN$ with right angle at $K$.

Step2: Identify common sides and angles

• $KN$ is a common side to both triangles, so $KN = KN$ (reflexive property).
• $\angle JKN$ and $\angle LKN$ are right angles, so $\angle JKN=\angle LKN = 90^{\circ}$.
• We also have $JN = LN$ (hypotenuse, assuming the triangle is isoceles or from the diagram context) and $KN$ is a leg.

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. Here, we can use HL to prove $\triangle JKN\cong\triangle LKN$.

Answer:

Hypotenuse - Leg (the option corresponding to Hypotenuse - Leg)