Question

determine if the triangles are congruent. if yes select the correct theorem. if no select not congruent
congruent select
theorem select

Explanation:

Step1: Identify right - angled triangles

We have two right - angled triangles $\triangle MON$ and $\triangle KON$ as $\angle MON=\angle KON = 90^{\circ}$.

Step2: Observe equal sides

We see that the hypotenuse $MN = KN$ (marked with the same number of ticks) and the common side $ON$ (shared between the two triangles).

Step3: Apply congruence theorem

By the Hypotenuse - Leg (HL) congruence theorem for right - angled triangles, since the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of the other right - angled triangle, $\triangle MON\cong\triangle KON$.

Answer:

Congruent: Yes
Theorem: Hypotenuse - Leg (HL)