Question

In the given figure, if ACFD and ABED are parallelograms, then which of the following statements are true?

• A. AC = DF
• B. AB = DE
• C. BC = EF
• D. All the above

Answer 1

The correct option is D

All the above

ACFD is a parallelogram ……. (given)

$CF=AD,CF\parallel AD$ and $AC=DF$………. (i)

ABED is a parallelogram …….. (given)

$AD=BE,AD\parallel AB$ and $AB=DE$ ……. (ii)

From equations (i) and (ii) we have,

$CF=BE$ and $CF\parallel BE$

$\Rightarrow$ BEFC is a parallelogram (One pair of opposite sides are equal and parallel)

Hence, BC = EF.

Hence, all the three statements are correct.