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Pythagorase teoreem (9. Klassile)

Pythagorase teoreem (9. Klassile). Malle Eglit C.R.Jakobsoni nim.Gümnaasium Viljandi maakond Koolitaja M.Anissimov. Pythagoras. Kreeka matemaatik ja filosoof Elas umbes 580-500.a.e.Kr. Tõestas juba Babüloonias umbes 2000.a.e.Kr. tuntud teoreemi. . c. a. •. . b.

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Pythagorase teoreem (9. Klassile)

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  1. Pythagorase teoreem(9. Klassile) Malle Eglit C.R.Jakobsoni nim.Gümnaasium Viljandi maakond Koolitaja M.Anissimov

  2. Pythagoras • Kreeka matemaatik ja filosoof • Elas umbes 580-500.a.e.Kr. • Tõestas juba Babüloonias umbes 2000.a.e.Kr. tuntud teoreemi

  3.  c a •  b Pythagorase teoreem: Täisnurkse kolmnurga kaatetite ruutude summa võrdub hüpotenuusi ruuduga. a2+ b2 =c2 +=90°

  4. B c   a •  c D E F • a   • C G a A •  a c c   H Tõestus Paneme neli võrdset täisnurkset kolmnurka kokku järgmiselt:

  5. B c   a a •  c D E F • a   • C G a A •  a c c   H • Tekkinud nelinurga ABDH kõik nurgad on +=90°. • Tekkinud nelinurga ABDH kõik küljed on c. • Järelikult on tekkinud nelinurk ABDH ruut.

  6. B c   a a •  c D E F • a  Täisnurkse kolmnurga pindala on  • C G a A •  a c c   H EF=FG=GC=CE=a-b Nelinurk EFGC on ruut. SEFGC=(a-b)2

  7. C2=(a-b)2+4· B c   a a •  c D E F • a   • C G a A •  a c c   H SABDH=SEFGC+4·SABC C2=a2-2ab+b2+2ab C2=a2+b2

  8. k y x s t m X= Näide1. Näide 2. Avalda x. Avalda y. X2+m2=k2 X2=k2-m2

  9. a b d d a a Pythagorase teoreemi rakendusi

  10. . a a

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