If two quadrilaterals are on the same base and between same parallel lines having same area prove that they are parallelogram
Answers
Answer:
They are not ║gm
Step-by-step explanation:
You cannot prove it. The two quadrilaterals may be two trapeziums which do not coincide, but still have same areas.
Proof:-
A (trapezium) =12(l1+l2)h, where
l1 and l2 are the parallel sides,
h = distance between the parallel sides.
Now, for any two trapeziums lying between the same parallels, their heights are equal.
Also, the two trapeziums are lying on the same base.
Hence, the second parallel sides for each trapezium need to be equal.
We can see that there are infinitely many such line segments on the same parallel which do not coincide.
Hence, the two trapeziums have equal areas.
Hence, the quadrilaterals need not be parallelograms.
Answer:
it is not necessary that they are parallelogram.