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. ∠a ≅ ∠m c. jl ≅ no d. kl ≅ om

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, we need a pair of corresponding sides to be equal.

Step2: Analyze each option

• Option A: $\overline{JK}=\overline{NO}$. If two angles of one triangle are equal to two angles of another triangle and the included side between those angles in one triangle is equal to the included side between the corresponding angles in the other triangle (ASA criterion), then the triangles are congruent.
• Option B: $\angle K=\angle M$. This just gives another angle - equality. We already have two pairs of angles equal, and adding another angle - equality does not prove congruence as we need a side - equality.
• Option C: $\overline{KL}=\overline{OM}$. If two angles of one triangle are equal to two angles of another triangle and the non - included side opposite one of the equal angles in one triangle is equal to the non - included side opposite the corresponding equal angle in the other triangle (AAS criterion), then the triangles are congruent.
• Option D: $\overline{JL}=\overline{MN}$. Similar to Option C, if two angles of one triangle are equal to two angles of another triangle and the non - included side opposite one of the equal angles in one triangle is equal to the non - included side opposite the corresponding equal angle in the other triangle (AAS criterion), then the triangles are congruent.

Answer:

A. $\overline{JK}=\overline{NO}$, C. $\overline{KL}=\overline{OM}$, D. $\overline{JL}=\overline{MN}$