Question

ABCD is a square prove that AC square =2AB square

Answer 1

it is given that ABCD is square so AB=BC=BD=AD...
THEN BY PYTHAGORAS THEROEM in triangle
ABC & ACD
NOW BY THIS WE CAN SAY THAT ACsq.=2ABsq.

Answer 2

By using pythagoras theorem ..in triangle ABC
AC
$ac {}^{2} = ab {}^{2} + bc {}^{2}$
hope this help you