Question

in a quadrilateral ABCD angle A + angleD is equal to 90 degree prove that AC square + BD square is equal to AD square + BC square​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

We have, ∠A + ∠D = 90°

In ΔAPD, by angle sum property,

∠A + ∠D + ∠P = 180°

 90° + P = 180°

 ∠P = 180° – 90° = 90°

In ΔAPC, by Pythagoras theorem,

AC2 = AP2 + PC2 ....(1)

In ΔBPD, by Pythagoras theorem,

BD2 = BP2 + DP2 ....(2)

Adding equations (1) and (2),

AC2 + BD2 = AP2 + PC2 + BP2 + DP2

 AC2 + BD2 = (AP2 + DP2) + (PC2 + BP2) = AD2 + BC2