∵AD⊥BC ∴AD^2=AB^2-BD^2 AD^2=AC^2-DC^2 ∵AD^2=BD*DC ∴(AB^2-BD^2)+(AC^2-DC^2)=2BD*DC ∴AB^2+AC^2=(BD+DC)^2 ∵BD+DC=BC ∴AB^2+AC^2=BC^2 ∴△ABC是直角三角形