in a traingle ABC ad perpendicular to bc prove that ab²+cd²= ac²+bc²
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When AD is drawn perpendicular to BC, twotriangles ADB and ADCare obtained.
Considering triangle ADB,
AB2= AD2+ BD2......(1) (using, Pythagoras theorem)
Considering triangle ADC,
AC2= AD2+ CD2(2) (using Pythagoras theorem)
Subtracting equation (2) from equation (1),
AB2-AC2= AD2+ BD2- (AD2+ CD2)
AB2- AC2= AD2+ BD2- AD2- CD2
AB2- AC2= BD2- CD2
AB² + CD² = AC² + BD² hence proved
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