" IN A RIGHT ∆ , THE SQUARE OF THE HYPOTENUSE IS EQUAL TO THE SUM OF THE SQUARE OF THE OTJER TWO SIDES . "
(PROVE PHYTOGOROUS THEROME )
(PROVE PHYTOGOROUS THEROME )
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Given :- A right triangle ABC right angled at B.
To prove :- AC^2 = AB^2+ BC^2
Proof :-
BD is perpendicular to AC
∆ ABD ~ ∆ ABC
AD/ AB = AB/ AC ••••••• ( sides are proportional )
AD• AC = AB^2 •••••••• (1)
∆ BDC ~ ∆ ABC
CD/ BC = BC/ AC
CD• AC = BC^2 •••••••(2)
Adding (1) and (2)
AD• AC + CD• AC = AB^2 + BC^2
AC ( AD + CD ) = AB^2+ BC^2
AC• AC = AB^2+ BC^2
AC^2 = AB^2+ BC^2
Hence proved•••••••
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