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. jk¯≅no¯ b. jl¯≅nm¯ c. kl¯≅om¯ d. ∠l≅∠m

Explanation:

Step1: Recall triangle - congruence criteria

We know that the Angle - Angle - Side (AAS) and Angle - Side - Angle (ASA) congruence criteria for triangles require side - length equalities along with angle - equalities. Given two pairs of equal angles in \(\triangle{JKL}\) and \(\triangle{NOM}\), we need a side - length equality.

Step2: Analyze each option

For option A: If \(\overline{JK}\cong\overline{NO}\), along with the two pairs of equal angles, we can use the ASA (Angle - Side - Angle) congruence criterion to prove \(\triangle{JKL}\cong\triangle{NOM}\). For option B: If \(\overline{JL}\cong\overline{NM}\), along with the two pairs of equal angles, we can use the AAS (Angle - Angle - Side) congruence criterion to prove \(\triangle{JKL}\cong\triangle{NOM}\). For option C: \(\overline{KL}\cong\overline{OM}\) is not a side that is between or opposite the given equal - angle pairs, so it will not help in proving the congruence. For option D: \(\angle{L}\cong\angle{M}\) is just an additional angle - equality, and we already have two pairs of equal angles, so this is not the side - length information we need.

Answer:

A. \(\overline{JK}\cong\overline{NO}\), B. \(\overline{JL}\cong\overline{NM}\)