Two pairs of perpendicular lines form four right triangles. Prove that the midpoints of the hypotenuses of these triangles are the vertices of a rectangle.
This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.
139. Let angles B and D of quadrilateral ABCD be right angles, and let E and F be the points of intersection of its pairs of opposite sides. Draw the line AC and establish that AC⊥EF. Prove that the midpoints of the hypotenuses are vertices of a quadrilateral, the sides of which are parallel to AC and EF.
Source: NuminaMath-1.5,
licensed Apache-2.0.
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