E and F are the middle of sides AB and BC of triangle ABC. Find EF and angle BEF, if AC = 14cm, angle A = 72 degrees.

1.) First, find the value of the segment EF.
By condition E and F are the midpoints of the sides AB and BC of the triangle ABC, respectively.
Thus, the segment EF is the middle line of the triangle ABC.
According to the rule, the middle line of the triangle is parallel to the third side, that is, the segment EF is parallel to AC.
Also, according to the rule, the length of the centerline of a triangle is equal to half the length of the side to which this centerline is parallel.
So it can be written.
EF = AC: 2.
EF = 14: 2.
EF = 7 (cm).
2.) Find the value of the angle BEF.
Since line AB intersects two parallel lines EF and AC, the corresponding angles are usually equal.
The angles EF and AC are corresponding by construction.
So the BAC angle is equal to the BEF angle.
So, you can write.
BAC = BEF = 72 °.
Answer: EF = 7 cm; BEF = 72 °.