Question

State the whether given statement is true or false

$ABCD$ is a parallelogram. $AB$ produced to $E$ so that $BE=AB$. Prove that the $ED$ bisects $BC$.

• A. True
• B. False

Answer 1

The correct option is A True

R.E.F image

$AB=BE$ To prove $:-BM=MC$

Since $AB=CD$ (ABCD is || gm)

also $AB=BE$

$\therefore BE=CD$ .....(1)

$\angle CDM=\angle BEM\left(CD||AE\right)$ .......(2)

$\angle CMD=\angle BME$ (vertically opposite angle) .....(3)

from (1), (2) and (3)

$\Delta CMD\cong \Delta BEM$ (By AAS)

$\therefore$ by $CPCT$

$BM=CM$