Question

20. If the two parallelograms have the same base and are between the same parallel lines then these two parallelograms must have Equal area b. Not equal a. perimeter d. equal d. C. angles​

Answer 1

A. Equal Area

If the two parallelograms have the same base and are between the same parallel lines then these two parallelograms must have Equal area.

Explanation:

If two parallelograms have same base and are between same parralel lines, then they have same areas.

Let's Proof it:

In the adjoining figure,

ABCD and ABEF are two parrallelograms, on the same base and between the same parallel lines.

Ar.(||gram ABCD) = Ar.(ΔADF) + Ar.(AFCB)

Ar.(||gram ABEF) = Ar.(ΔBEC) + Ar.(AFCB)

In ΔADF and ΔBEC,

AD = BC (opposite sides of a parallelogram are equal)

AF = BE (opposite sides of a parallelogram are equal)

L ADF = L BCE (Corresponding angles on two parallel lines are equal)

Therefore, ΔADF ≈ ΔBEC

Hence, ar.(ΔADF) = ar.(ΔBEC) ........ (iii)

Also,

Ar.(||gram ABCD) = Ar.(ΔADF) + Ar.(AFCB) .....(i)

Ar.(||gram ABEF) = Ar.(ΔBEC) + Ar.(AFCB) ......(ii)

By, equation (i), (ii), and (iii), we get

ar.(||gram ABCD) = ar.(||gram ABEF)

Hence, proved.