Question

In a triangle ABC, D is the midpoint of BC : AD is produced up to E so that DE= AD.
then AB=EC

• A. True
• B. False

Answer 1

The correct option is A True

Given :

In $△ABC$, AD is the median.

AD is produced to E such that $AD=ED$.

Now, in $△ABD$ and $△ECD$,

$BD=CD$ (AD is the median)

$\angle ADB=\angle EDC$ ( Vertically opposite angles )

$AD=ED$ ( Given )

So, $△ABD\cong △ECD$.

Therefore, $AB=EC$ ( By CPCT).