1 / 8

Teorema lui Thales

Teorema lui Thales. Baza geometriei Clasa VII-a. Grecu Ioan. Fie ABC un triunghi oarecare , B’ Є ﴾ AB ﴿ C’ Є ﴾ AC ﴿. A. B’. C’. C. B. B’C’ ║ BC. Dac ă :. A. B’. C’. B. C. Atunci :. AB ’ = AC’ AB AC. Demonstra ţie. Se traseaz ă : B’E ┴ AC C ’D ┴ AB

dorjan
Télécharger la présentation

Teorema lui Thales

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Teorema lui Thales Baza geometriei Clasa VII-a Grecu Ioan

  2. Fie ABC un triunghi oarecare , B’ Є﴾AB﴿ C’ Є﴾AC﴿ A B’ C’ C B

  3. B’C’ ║ BC Dacă: A B’ C’ B C Atunci: AB’ = AC’ AB AC

  4. Demonstraţie Se trasează : B’E ┴ AC C’D ┴ AB BM ┴ B’C’ şi CN ┴ B’C’ A D ┌ E ┐ C’ M N B’ -------------------- ┘ └ B C

  5. AB’ · C’D 2 AB’ = = ﴾1﴿ BB’ · C’D BB’ TAB’C’TC’BB’ 2 AC’ · B’E TAB’C’TB’C’C 2 AC’ ﴾2﴿ = = CC’ CC’ · B’E 2

  6. În dreptunghiul BCNM=> BM ═ CN => = > T BB’C’ = T CC’B’ ﴾3﴿ BM · B’C’ CN · B’C’ = 2 2 AC’ AB’ Din (1), (2), (3) = > = = = > BB’ CC’ AB’ AC’ AC’ AB’ = = > = BB’ + AB’ AB CC’ + AC’ AC

  7. În dreptunghiul BCNM=> BM ═ CN =>=> = > T BB’C’ = T CC’B’ ﴾3﴿ BM · B’C’ CN · B’C’ = 2 2 A B’ C’ M N B C

  8. Din (1), (2), (3)= > AC’ AB’ = = = > BB’ CC’ AB’ AC’ = > = BB’ + AB’ CC’ + AC’ AB’ AC’ = > = AB AC

More Related