Question

in the given figure <bac=90 and AD perpendicular to BC prove that AB^2+CD^2=BD^2+AC^2

Answer 1

your answer is here....

Answer 2

OK
here is the solution
let's take Δ ADB
since angle D = 90°
=> AD²+BD²=AB² (Pythagoras theorm)
=>AD²=AB²-BD² .......................(1)

take Δ ADC
since angle D is 90
=> AD²+CD²=AC² (Pythagoras theorm)
=>AD²=AC²-CD² .......................(2)

BY (1) and (2)
=> AB²- BD²= AC²- CD²

shift BD² and CD² to either side
=> AB²+CD²=BD²+ AC²

HENCE PROVED

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