Respuesta :

Answer:

  1. ⇒ a²+b² = c²

Step-by-step explanation:

  1. in ΔBCD and ΔBAC
  2. ∠BDC = ∠ACB (90° each)
  3. ∠CBD =∠CBA (common)
  4. by AA similarity criteria
  5. ΔBCD  is similar to ΔBAC
  6. BC/BA = CD/AC = BD/BC ( by similarity creteria)
  7. BC/BA =BD/BC
  8. BC² = BD* BA (equation 1)
  9. Again, in ΔACD & ΔABC
  10. ∠CDA = ∠ACB (90° each)
  11. ∠CAD = ∠CAB (common)
  12. By AA similarity criteria
  13. ΔACD is similar to ΔABC
  14. AC/AB = CD/BC = AD/AC (by similarity criteria)
  15. AC/AB = AD/AC
  16. AC² = AD·AB (equation 2)
  17. Adding equation 1 & equation 2
  18. BC²+AC² = (BD.BA) + (AD.AB)
  19. BC²+AC² = AB(BD+AD)
  20. BC²+AC² = AB.AB   (BD+AD=AB)
  21. BC²+AC² = AB²
  22. ⇒ a²+b² = c²
  23. Hence Proved

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