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Question
If a diagonal of a quadrilateral bisects both the angles, then it is a ______.
Options
kite
parallelogram
rhombus
rectangle
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Solution
If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.
Explanation:
A parallelogram is a quadrilateral whose diagonal bisects both angles. It is also true for rhombus and rectangle but in a rhombus all the sides are also equal and in a rectangle all the angles are also equal.
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RELATED QUESTIONS
Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
Diagonals of parallelogram ABCD intersect at O as shown in the following fegure. XY contains O, and X, Y are points on opposite sides of the parallelogram. Give reasons for each of the following:
(i) OB = OD
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(iii) ∠BOY = ∠DOX
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Now, state if XY is bisected at O.

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It can be a square.
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
Fill in the blank, in the following, so as to make the statement true:
The diagonals of a rhombus ...... each other at ...... angles.
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If the adjacent sides of a parallelogram are equal then parallelogram is a ______.
