"Question 3 Can a quadrilateral ABCD be a parallelogram if (i)∠D +∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii)∠A = 70° and∠C = 65°?
Understanding Quadrilaterals Page 51"
Answers
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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Hope this will help you....
Answer:
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:
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.
========================================================
Hope this will help you....
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