Question

cw: triangle congruence theorems
if not congruent, write none in both slots.
these triangles can be proven congruent by □ △lmk ≅ □ △

Explanation:

Step1: Identify the congruent triangles

We have two triangles \( \triangle LMK \) and \( \triangle JKM \).

Step2: Check the congruence criteria

We know that \( JK = LM \) (given by the marks on the sides). \( KM=MK \) (common side). Also, \( \angle LMK=\angle JKM \) and \( \angle LKM = \angle JMK \) (given by the angle - marks). By the Angle - Side - Angle (ASA) congruence theorem, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Answer:

These triangles can be proven congruent by \( ASA \). \( \triangle LMK\cong\triangle JKM \)