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Question

If the diagonal BD of a parallelogram bisects B and D, then ABCD is a



A

Rectangle

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B

 Rhombus 

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C

Square

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D

Trapezium

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Solution

The correct option is B

 Rhombus 


ABCD is a parallelogram (given)

    B = D = 2x° (say)  … (opposite angles of a parallelogram are equal)

Therefore ADB =BDC = ABD = DBC = x° ....(DB bisects B and D)

ADBis isosceles …...(base angles are equal to x°)

Therefore, AD = AB  ……. (equal sides of an isosceles triangle)

ABCD is a rhombus ….. (all sides of the parallelogram are equal)

Hence (B)


Mathematics

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