The trapezoid with parallel sides and is drawn on the plane. Using only ruler construct triangle with the area equals to the area of trapezoid.
Solution
We first construct the point of the intersection of diagonals, and the point of intersection of sides and . It is well known that contains midpoints and of parallel sides (fig. 11). We have . Hence and are parallelograms, and are the points of intersection of their diagonals respectively. We can draw the line which is a midline of trapezoid and intersects two sides at and respectively. We then draw line , that intersects at point . Thus is desired, since .
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