Question

It is given that BDEF and FDCE are parallelograms. Prove that BD = CD.

Answer 1

Hint:
 In this question, we are given a figure in which BDEF and FDCE are parallelograms. In the triangle ABC, we need to prove BD to be equal to CD. For this we will use the property of parallelogram according to which opposite sides of a parallelogram are parallel and equal and hence conclude our result.

Complete step by step answer:
Here we are given the following diagram in which we have a triangle ABC. E, F, D are points on the sides AC, AB, and BC respectively.

Here we have BDEF and FDCE as parallelograms. Let us first take the parallelogram BDEF.
We know that in a parallelogram opposite sides are equal and parallel. So we can say that, in the parallelogram BD is equal to EF i.e., BD = EF . . . . . . . . . . . . . (1)
Now let us observe the parallelogram FDCE. Again using the property of parallelogram that, opposite sides are equal and parallel. We get EF as equal to CD i.e., EF = CD . . . . . . . . . . . (2).
From (1) and (2) we observe that, EF = BD = CD
We can also write it as BD = CD.
Hence we have proved that BD = CD
Note:
Students should keep in mind all the properties of parallelogram. Note that opposite sides of a parallelogram are always parallel and equal. So here we can also say FB = ED from parallelogram BDEF and we can also say that FD = ED from parallelogram FECD.