# In triangle ABC, point M is the midpoint of side AB and angle A is equal to angle B.

In triangle ABC, point M is the midpoint of side AB and angle A is equal to angle B. Prove that angle ACB is equal to 2 angle AFM.

Let’s take a look at the figure to solve it.

By condition, the angles CAB and CBA are equal to each other, therefore, the triangle ABC is isosceles, in two angles.

Since, according to the condition, point M divides AB into equal parts, AM = BM, the straight line drawn from point C to point M is the height, median and bisector of triangle ABC, according to the properties of an isosceles triangle.

Angle АСВ = АСМ + ВСМ.

The bisector CM divides the angle into two equal angles, AFM = BCM, therefore, ASB = 2 * AFM, which was required to prove. 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.