Through vertex C of triangle ABC, a line p is drawn parallel to line ABC.

Through vertex C of triangle ABC, a line p is drawn parallel to line ABC. Prove that all triangles with vertices on line p and base AB have equal areas.

In triangle ABC, draw the height CH, which is perpendicular to the side AB and line P.

On the line P, mark the point C1. In the triangle ABC1, the base AB, the height of its CH, then:

Savs1 = AB * CH / 2.

On the line P, mark the point C2. In the triangle ABC2, the base AB, the height of its CH, then:

Savs2 = AB * CH / 2.

Consequently, for all triangles with base AB and vertex Cn taken on the line P, the area will be equal to AB * CH / 2 cm2, which was required to prove.