Question

In a $\Delta ABC$, BD is the median to the side AC, BD is produced to E such that BD = DE.

Hence, AE parallel to BC.

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $△ABC$, BD is median on AC. BD produced to E $BD=DE$.
To prove: $AE\parallel BC$
In $△AED$ and $△BDC$,
$\angle ADE=\angle BDC$ (Vertically opposite angles)
$AD=DC$ (D is mid point of AC)
$BD=DE$ (Given)
Hence, $△AED\cong △BEC$ (SAS rule)
Thus, $\angle DAE=\angle DCB$ (By cpct)
but these are alternate angles w.r.t. AE and BC. Hence, $AE\parallel BC$