Question

simple proof for Pythagoras theorem

Answer 1

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In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

GIVEN :- A right triangle ABC right angled at B.

TO PROVE :- AC^2= AB^2+ BC^2

PROOF :- BD is perpendicular to AC

∆ ADB~ ∆ ABC

AD/ AB= AB/ SC ••••••••••••• ( 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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Answer 2

Step-by-step explanation:

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