# Parallelogram ABCD. The bisectors of angles A and D intersect at point K on the BC side.

September 20, 2021 | education

| **Parallelogram ABCD. The bisectors of angles A and D intersect at point K on the BC side. The side is 40. You need to find the sun.**

Since AK is the bisector of the angle BAD, the angle ABK = DAK.

In a parallelogram, the opposite sides are parallel, then the angle AKВ = DAK as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AK.

Then in the triangle ABK the angle BAK = BKA, and then the triangle ABK is isosceles with the base AK.

Then BK = AB = 40 cm.

Similarly, the triangle CDK is isosceles, CK = CD = 40 cm.

Then BC = BK + СK = 40 + 40 = 80 cm.

Answer: The length of the BC side is 80 cm.

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.