11. Determine if the two triangles are congruent. Justify your answer.

Analysis:

• Triangle 1 (left, triangle LMK): Has an angle of 130° at M. Sides LM and MK are marked with single tick marks, indicating they are equal. Side KN is marked with a double tick mark.
• Triangle 2 (right, triangle ABC): Has an angle of 80° at B. Sides AB and BC are marked with single tick marks, indicating they are equal. Side AC is marked with a double tick mark.
• We have two sides and a non-included angle (SSA) for triangle LMK (LM = MK, angle LMK = 130°). We have two sides and an included angle for triangle ABC (AB = BC, angle ABC = 80°).
• Comparing the triangles: We have two sides equal (LM=MK and AB=BC). However, the angles given are 130° and 80°, and the sides adjacent to these angles are not necessarily equal, nor are the third sides necessarily equal. The marking of KN and AC with double ticks might imply they are equal, but we don't have enough information about the angles relative to these sides for congruence. Even if KN=AC, the SSA case is ambiguous and doesn't guarantee congruence.

Answer: No, the two triangles are not necessarily congruent. We have Side-Side-Angle (SSA) information for the first triangle and Side-Angle-Side (SAS) information for the second triangle, but the specific values and their relationships do not lead to congruence.