What is Pythagoras theorem in mathematics
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Step-by-step explanation:
in a right angle triangle the square of the hypotenuse is a sum of the squares of other two sides
Given-triangle abc
B-90
To prove-AC²+=AB²+BC²
Construction-draw BD perpendicular to AC
Proof- In triangle ADB and triangle ABC
La=La(common)
L ADB=L ABC(90°)
=>Triangle ABC ~ triangle ABC
AD\AB= AB/AC
AD×AC= AB×AB••••••[1]
In triangle BCD and triangle ACB
LC=LC(common)
LBDC =LABC(90°)
LBDC~LACB
BC/AC= CD/BC
AC×CD= BC×BC••••••••[2]
From (1)&(2)
AD×AC+AC×CD=AB²+BC²
AC(AD+CD)=AB²+BC²
AC×AC=AB²+BC²
AC²=AB²+BC²
Hence proved
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The pythagoras theorem states that in every right angle triangle the sum of the square of two legs is less than the square of the hypotenuse.
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