Question

1. kim draws a triangle with one 4 mm side, one 6 mm side, and a 25° included angle between those sides. if you follow the same steps as kim to draw a triangle, is your triangle congruent to kim’s triangle? explain. yes. it is only possible to construct one triangle when given two sides and an included angle. yes. it is possible to construct two triangles when given two sides and an included angle. no. it is possible to construct three triangles when given two sides and an included angle. no. it is not possible to construct one triangle when given two sides and an included angle.

Explanation:

The SAS (Side-Angle-Side) congruence rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Following the exact steps as Kim means replicating the two sides (4 mm, 6 mm) and the included 25° angle, so only one unique triangle can be constructed, which is congruent to Kim's.

Answer:

Yes. It is only possible to construct one triangle when given two sides and an included angle.