. Two parallelograms ABCD and ABEF are in the same side of AB and area of parallelogram ABEF > area of parallelogram ABCD. Prove that (a) DCEF is a parallelogram (b) area of parallelogram DCEF = area of parallelogram ABEF- area of parallelo- gram ABCD
Answers
Step-by-step explanation:
Given that ABEF is a rectangle and ABCD is a parallelogram, with the same base AB and have equal areas.
Since ∥gm & rectangle have equal areas with same base AB, thereore it will be between same set of ∥al lines.
AB=CD⟶(1) [opposite sides of the ∥gm]
AB=EF⟶(2) [opposite sides of rectangle]
from (1) & (2), we get
CD=EF⟶(3)
In △ADF,
∠AFD=90
0
AD>AF [∵ Hypotenuse is greater than other sides.] ⟶(4)
BC>BE [Since BC=AD and BE=AF] ⟶(5)
Perimeter of ∥gm ABCD =AB+BC+CD+DA
=AB+BC+EF+DA [from equation (3)]
>EF+FA+AB+BE [Using (5)]
which is the perimeter of rectangle ABEF.
Therefore perimeter of ∥gm with the same base and with equal areas is greater than the perimeter of the rectangle.
∴ Perimeter ABCD > Perimeter ABEF