Question

ABCD is a square prove that AC square is equal to 2 a b square​

Answer 1

Step-by-step explanation:

AC is the diagonal of square ABCD

AC divide the square in two congruent right angle triangle. as all angles of square is 90°

therefore with AC we get a right angle triangle ABC

AB and BC are equal sides and AC is hypotenuse

by Pythagoras theorem

${hyp}^{2} = {adj}^{2} + {opp}^{2} \\ {ac}^{2} = {ab}^{2} + {bc}^{2} \\ {ac}^{2} = {ab}^{2} + {ab}^{2} \: \: \: (ab \: = bc) \\ {ac}^{2} = 2{ab}^{2} \\ hence \: proved$