Question

what additional piece of information is needed to prove △jkl≅△nom? which of the following additional congruencies, by themselves, will be sufficient to prove △jkl≅△nom? select all that apply. a. ∠j≅∠n b. kl≅om c. jl≅nm d. jk≅no

Explanation:

Step1: Recall triangle - congruence criteria

The main triangle - congruence criteria are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles). Given two pairs of angles are equal (marked in the figure), we need a side - congruence.

Step2: Analyze each option

• Option A: $\angle J\cong\angle N$ is already given by the angle - markings, so it is not additional information for congruence.
• Option B: $\overline{KL}\cong\overline{OM}$ is a non - corresponding side, so it won't help in proving $\triangle{JKL}\cong\triangle{NOM}$.
• Option C: $\overline{JL}\cong\overline{NM}$ is a corresponding side. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle (ASA criterion), then the triangles are congruent. Here, with the given two pairs of angles and this side - congruence, we can prove $\triangle{JKL}\cong\triangle{NOM}$.
• Option D: $\overline{JK}\cong\overline{NO}$ is a corresponding side. If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle (AAS criterion), then the triangles are congruent. With the given two pairs of angles and this side - congruence, we can prove $\triangle{JKL}\cong\triangle{NOM}$.

Answer:

C. $\overline{JL}\cong\overline{NM}$, D. $\overline{JK}\cong\overline{NO}$