Teorem Pythagoras

Gambaran teorem Pythagoras

Id gana matematik (geometri), teorem Pythagoras nopo nga' Teorem ii popiungkait do kotolu-tolu disan id suang do Segi tiga bersudut tegak. Tumanud do teorem diti, kuasa duo montok hipotenus (gorisan sendeng) segiti kisudut tegak nopo nga' miagal miampai asil poruhangan kuasa dua montok duo disan suai.

Soroho nopo do c nopo nga' ninaru hipotenus, a om b nopo nga' ninaru duo disan di noolu, piagal dilo milo wonsoyon:

$a^{2}+b^{2}=c^{2}\,$

om c milo hongkumon sabaagi:

$c={\sqrt {a^{2}+b^{2}}}.\,$

Pembuktian momoguno segi tiga tegak

${\frac {d}{a}}={\frac {a}{c}}\quad \Rightarrow \quad d={\frac {a^{2}}{c}}\quad (1)$

${\frac {e}{b}}={\frac {b}{c}}\quad \Rightarrow \quad e={\frac {b^{2}}{c}}\quad (2)$

Mantad gambal $c=d+e\,\!$. Om miampai poposimban piagalam (1) om (2):

$c={\frac {a^{2}}{c}}+{\frac {b^{2}}{c}}$

Popoundali montok c:

$c^{2}=a^{2}+b^{2}\,\!.$

Intangai nogi

• Hukum kosinus

Popioput soliwan

• Teorem Pythagoras di MathWorld
• 75 bukti teorem Pythagoras