Point O and F lie on sides AB and BC of triangle ABC, respectively.

Point O and F lie on sides AB and BC of triangle ABC, respectively. Prove that lines FO and AC are parallel if AB = 48cm, CB = 32cm. AO = 18cm, BF = 20cm.

1. Calculate the length of the segment BО:

BO = AB – AO = 48 – 18 = 30 centimeters.

2. Find the ratio of the sides of triangles ABC and OBF:

AB / BО = 48/30 = 1.6.

BC / BF = 32/20 = 1.6.

3. Based on the results of the calculations, we conclude that the two sides of one are proportional to the two sides of the other.

∠В belongs to triangle ABC and triangle BOF (common).

Hence the above triangles are similar.

4. From the similarity of triangles it follows that the side ОF is parallel to the side АС, which was required to prove.

Answer: The OF side is parallel to the AC side.