Question

на сторонах ab и bc трикутника abc взято точки e і f відповідно так,що ef паралельно ac. Знайдіть ab якщо ef=5см, be=4см, ac=8см

Answer 1

This is a problem that can be solved using the parallel lines and transversals theorem. The theorem states that if two lines are parallel and a transversal intersects them, then corresponding angles are congruent and alternate interior angles are congruent.

In this problem, we can consider line EF parallel to line AC, and line AB as a transversal. Therefore, we have:

∠EAB = ∠FAC (corresponding angles)

∠EBF = ∠FAC (alternate interior angles)

Now, we can use the following proportionality:

AB/BE = AC/EF

AB = (AC * BE) / EF

By substituting the given values into the equation we get:

AB = (8cm * 4cm) / 5cm

AB = 3.2cm

Therefore, AB=3.2cm