Question

in a triangle abc ad is perpendicular to bc prove that ab square+cd square=ac square+bd sq​

Answer 1

From triangle ADB,

ABsq = ADsq + BDsq

=>ADsq =ABsq - BDsq --------1

From triangle ADC,

ACsq =ADsq + DCsq

=>ADsq=ACsq - DCsq ---------2

From 1 & 2

ABsq -BDsq = ACsq - DCsq

=>ABsq + DCsq = ACsq + BDsq

=>ABsq +CDsq = ACsq +BDsq

PROVED