Answer: Since it is a equilateral triangle all sides are equal

Step-by-step explanation:

i.e, AB=BC=AC

By ASA postulate ABN congruent to ANC so by CPCT

BN=CN

BC=2BN

By pythagoras theorem

AN²=AB²-BN²

AN²=BC²-BN² AB=BC

AN²=(2BN)²-BN² BC=2BN

AN²=4BN²-BN²

AN²=3BN²

Hence proved