A straight line parallel to side MN of triangle MNK intersects sides KM and KN at points E and F

univerkov | September 27, 2021 | education

A straight line parallel to side MN of triangle MNK intersects sides KM and KN at points E and F, respectively, KE = 6 cm, KM = 10 cm, KF = 9 cm, KN = 15 cm, MN = 20 cm. What is side EF equal to?

Since the segment EF is parallel to MH, the triangles MKN and EKF are similar in two angles.

The angle K for triangles is common, the angle НМК = FEK as the corresponding angles at the intersection of parallel lines МН and EF of the secant MC.

Let’s determine the coefficient of similarity of triangles. K = KE / KM = 6/10 = 3/5.

Then EF / MH = 3/5.

EF = 3 * MN / 5 = 3 * 20/5 = 12 cm.

Answer: The length of the segment EF is 12 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.