The bases of the trapezoid ABCD are 10 cm and 6 cm. The sides AB and CD are extended until they intersect at point F.

| February 21, 2021 | education

The bases of the trapezoid ABCD are 10 cm and 6 cm. The sides AB and CD are extended until they intersect at point F. Find the length of the segment FB if side AB is 6 cm.

Let the length of the segment BF = X cm, then the length of the segment AF = (AB + X) = (6 + X) cm.

Let us prove that triangles AFD and BFC are similar.

The angle F for triangles is common, the angle FAD of the triangle FAD is equal to the angle FВD, as are the corresponding angles at the intersection of parallel lines AD and BC secant AF. Triangles AFD and BFC are similar in the first sign of similarity – in two angles.

Then AD / BC = AF / BF.

10/6 = (6 + X) / X.

6 * (6 + X) = 10 * X.

36 + 6 * X = 10 * X.

4 * X = 36.

X = 36/4 = 9 cm.

ВF = 9 cm.

Answer: The length of the segment BF = 9 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.