In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Figure). Show that:
ABCD is a rectangle in which diagonal AC bisects as well as . Show that:
(i) ABCD is a square (ii) diagonal BD bisects as well as .
Diagonal AC of a parallelogram ABCD bisects (See figure). Show that
(i) it bisects also,
(ii) ABCD is a rhombus.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
Show that the diagonals of a square are equal and bisect each other at right angles.