In parallelogram ABCD, line AM is drawn, intersecting the diagonal BD at point K. Find BM: BC if BK: KD = 2: 3.

univerkov | September 18, 2021 | education

Since the opposite sides of the parallelogram are equal, AD = BC.

Let us prove that triangle AKD and BKM are similar.

Angle BKM = AKD as vertical angles at the intersection of straight lines BD and AM.

Angle КАD – ВМК as criss-crossing angles at the intersection of parallel ВМ and АD secant АМ, then the triangles VKM and AKD are similar in two angles.

Then: BM / AD = BK / KD.

BM / AD = 2/3.

BM / BC = 2/3.

Answer: BM / BC = 2/3.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.