CBSE Class 10 Answered

In right triangle ACE, we have

AC² + CE² = AE²                    (1)

In right triangle DCB, we have

DC² + CB² = DB²                  (2)

In right triangle ABC, we have

AC² + CB² = AB²                  (3)

From (1) and (2), we have

AE² + DB² = AC² + CE² + DC² + CB²

                   = AB² + CE² + DC²           ( from (3))

                  = AB² + DE²                    (by using the pythagoras theorem in right triangle DCE)

Thus, AE² + DB² = AB² + DE² 

Hence proved.