prove pythagores theorem

1.	prove pythagores theorem
Answer» Data :Consider a right angled triangle ABC right angled at bTo prove: hypotenuse square=base square + altitude squareConst: draw a perpendicular from b on side ac and name as d Proof:consider ∆abd and ∆abc They are similar by aa criteria AB/AD=AC/AB. (Cpst) Implies AB²=AC×AD...........(1)SIMILARLY consider ∆abc and ∆bdcThey are similar by aa criterionBy cpst AC/BC=BC/DCBC²=AC×DC...............(2)Adding 1 and 2AB²+BC²= AC×BC+AC×ADAB²+BC²=AC(BC+AD)AB²+BC²=AC(AC)AB²+BC²=AC²HENCE PROVED

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