In triangle ABC, point M is the midpoint of side BC. On the straight line AM, a point K is taken such that MK

In triangle ABC, point M is the midpoint of side BC. On the straight line AM, a point K is taken such that MK = AM. Prove that a quadrilateral ABKS is a parallelogram.

According to the condition, point M is the middle of the side BC of the triangle ABC, then the segment AM = CM. Also, by condition, the segment AM = KM.
Point M is the midpoint of the segments BC and AK, then according to the third criterion of a parallelogram, if a quadrangle has the diagonals at the intersection point divided in half, then such a quadrangle is a parallelogram, which was required to be proved.