Question

11/14 - triangle congruence schoology assignment
possible points: 0.58
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. (overline{jl}congoverline{nm})
□ b. (∠lcong∠m)
□ c. (overline{kl}congoverline{om})
□ d. (overline{jk}congoverline{no})
□ a.
□ b.
□ c.
□ d.

Explanation:

Step1: Recall triangle congruence theorems (AAS, ASA, SAS)

We know that for triangle congruence, we have theorems like AAS (Angle - Angle - Side), ASA (Angle - Side - Angle), and SAS (Side - Angle - Side). In \(\triangle JKL\) and \(\triangle NOM\), we already have two angles congruent (from the given angle markings).

Step2: Analyze each option

• Option A (\(\overline{JL}\cong\overline{NM}\)):

If \(\overline{JL}\cong\overline{NM}\), we cannot use any of the congruence theorems (AAS, ASA, SAS) directly. Because the side is not in the correct position relative to the known angles.

• Option B (\(\angle L\cong\angle M\)):

If \(\angle L\cong\angle M\), we still do not have a side - angle - side or angle - side - angle or angle - angle - side combination that satisfies the congruence theorems.

• Option C (\(\overline{KL}\cong\overline{OM}\)):

If \(\overline{KL}\cong\overline{OM}\), using the AAS (Angle - Angle - Side) theorem. In \(\triangle JKL\) and \(\triangle NOM\), we have two angles (given in the figure) and a non - included side (\(\overline{KL}\) and \(\overline{OM}\)).

• Option D (\(\overline{JK}\cong\overline{NO}\)):

If \(\overline{JK}\cong\overline{NO}\), using the AAS (Angle - Angle - Side) theorem. In \(\triangle JKL\) and \(\triangle NOM\), we have two angles (given in the figure) and a non - included side (\(\overline{JK}\) and \(\overline{NO}\)).

Answer:

C. \(\overline{KL}\cong\overline{OM}\), D. \(\overline{JK}\cong\overline{NO}\)