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

EF divides sides AB and BC in half, which means EF is the middle line, which means EF ∥ AC.

The obtained ∆ABS and ∆EBF are similar in the 2nd criterion of similarity: AB / EB = BC / BF = 2, ∠В – common.

Hence it follows that ∠A = ∠E = 72 °.

Since EF is the middle line, it is parallel to the third side and equal to half of it. Those. EF = ½ * AC.

Find EF = ½ * 14 = 7.

Answer: ∠Е = 72 ° and EF = 7.