E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Question

TextSquare as Special ParallelogramDiagonals of Parallelogram Bisect Each Other

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ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

Show that the diagonals of a square are equal and bisect each other at right angles.

Square as Special Parallelogram

ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (i) ABCD is a square (ii) diagonal BD bisects ∠ B as well as ∠ D.

Diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90º and ∠BDC = 50º, then ∠OAB is

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is

ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is