In triangle ABC, sides AB and BC are equal. Points M, H and K are midpoints of sides

In triangle ABC, sides AB and BC are equal. Points M, H and K are midpoints of sides AB, BC, AC, respectively. Prove that triangle AMK is equal to triangle KHC

By condition: | AB | = | BC | the line segments connecting the midpoints of the sides of the triangle are the midlines of the triangle and are equal to half of the parallel side. Therefore | MK | = 1/2 | BC |, | MH | = 1/2 | AC |, | HK | = 1/2 | AB |.

In a triangle AMK side | AM | is equal to the side | HK | of the triangle KHC. | MK | = | HC |, | AK | = | KC |.

It turns out that three sides of triangle AMK are equal to three sides of triangle AMK.

Q.E.D.