3. Can a quadrilateral ABCD be …

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3. Can a quadrilateral ABCD be a parallelogram, if: (i) D + B = (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

Posted by Gayathri B 5 years, 4 months ago

CBSE > Class 08 > Mathematics

1 answers

Gaurav Seth 5 years, 4 months ago

A quadrilateral is a parallelogram if

i)Its opposite sides are equal

ii) its opposite angles are equal

iii) diagonals bisect each other

iv) a pair of opposite sides is equal and parallel.

v) The sum of the adjacent angles should be 180∘

=========================================================

Solution:

if ∠D + ∠B = 180°, a quadrilateral ABCD may or may not be a parallelogram

but it should also fulfilled some conditions which are as:

The sum of the adjacent angles should be 180∘

Opposite angles must be of equal length.

(ii) No, opposite sides should be of same length. Here, opposite sides are of different lengths. AD ≠ BC

(iii) No, opposite angles should be of same measures. Here opposite angles are of different measures. ∠A ≠ ∠C.

0Thank You

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