Question

3.
(iv)
Can a quadrilateral ABCD be a parallelogram if
(i) ZD + ZB = 180°?
(ü) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(ii) ZA = 70° and ZC = 65°?​

Answer 1

$\large{\mathbb{\purple{\boxed{\green{\underbrace{\overbrace{\red{\boxed{\red{♪Answer♪}}}}}}}}}}$< />$\sf\huge\bold\red{༄❁❁❁❁❁༄ }$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∘

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Solution:

i)

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.

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