BdMO National Junior 2007/2

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Junior 2007/2

Unread post by samiul_samin » Sun Feb 24, 2019 12:51 am

In this figure there is a square inscribed in another square.Using this figure derive the Pythagorean Theorem.
Screenshot_2019-02-24-00-47-33-1.png

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Junior 2007/2

Unread post by samiul_samin » Sun Feb 24, 2019 12:56 am

By using this diagram we can say that:
Screenshot_2019-02-24-00-52-39-1.png
$(a+b)^2=4\times \dfrac 12\times ab+c\times c\Rightarrow a^2+b^2+2ab=c^2+2ab\Rightarrow a^2+b^2=c^2$

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