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Q.

The diagonals of a parallelogram bisect each other.


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a

True

b

False 

answer is A.

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Detailed Solution

Suppose ABCD is a parallelogram. Thus,
AB || DC and,
AD||BC
In ΔAOD and ΔCOB
https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/515/content_quadrilateral_22.png∠DAO = ∠BCO (Alternate angles)
AD = BC (opposite sides of a parallelogram)
∠ADO = ∠CBO (Alternate angles)
Hence, these two triangles are congruent by the angle side angle congruency.
In the congruent triangle
AO = OC and
BO = OD (corresponding sides)
Therefore, parallelogram’s diagonals bisect each other.
Hence, option 1 is correct.
 
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