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

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TextSquare as Special ParallelogramNCERT Textbook

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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.

TextSquare as Special ParallelogramDiagonals of Parallelogram Bisect Each Other

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

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Square as Special Parallelogram

Diagonals of Parallelogram Bisect Each Other

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.

CASE_STUDIESSquare as Special Parallelogram

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.

TextSquare as Special Parallelogram

ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

TextSquare as Special Parallelogram