Question

ABCD is a parallelogram.In which side AB to produced to E so that BE=AB.prove that ED bisects BC

Answer 1

REF.Image.

As, $AB=BE$

$B$ is mid point of $AE$

Consider $△EAD$

From midpoint Theorem

$BM=\frac{1}{2}AD$ (As$AD\parallel BM)$ & B is mid point of AE

$\Rightarrow =\frac{1}{2}BC$ (As AD = BC for parallelogram)

$\Rightarrow$ M is midpoint of BC

Hence $ED$ bisects $BC$