Question

Rhombus is the polygon that we get if the diagonals of a quadrilateral bisect each other at right angles.

• A. True
• B. False

Answer 1

The correct option is A

True

Consider the diagonals, AC and BD of quadrilateral ABCD.

They bisect each other at right angles.

$\therefore$ AC is the perpendicular bisector of line segment BD

$\Rightarrow$ AB = AD and CB = CD …(i)

And BD is the perpendicular bisector of line segment AC

$\Rightarrow$ AB = BC and AD = DC …(ii)

From (i) and (ii), we get

AB = BC = CD = AD

$\Rightarrow$ quadrilateral ABCD is a rhombus

Since, ABCD is a quadrilateral whose diagonals bisect each other at right angles and all four sides are equal.