E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
Show that the diagonals of a square are equal and bisect each other at right angles.
A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.
ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.
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