The diagonals of the parallelogram ABCD intersect at point O, and point F is the midpoint of side AB.

The diagonals of the parallelogram ABCD intersect at point O, and point F is the midpoint of side AB. a) Prove that triangles AFO and ABC are similar. b) Is it true that triangle FBO and ABD are similar?

The diagonals of the parallelogram at point O are divided in half, then OA = OC.

In triangle ABD, AF = BF by condition, OA = OC by construction, then the segment OF is the middle line of triangle ABC, which means that OF is parallel to BC.

Then, in triangles ABC and AFO, angle A is common, angle ABC = OFA as the corresponding angles at the intersection of parallel lines OF and BC secant AB, which means that triangles ABC and AFO are similar in two angles, which was required to be proved.

In triangles FBO and ABD are similar to OF parallel to AD, and the triangles are similar in two angles.