Question -
Answer -
Given, D and E are points on the sides CA andCB respectively of a triangle ABC right angled at C.
By Pythagoras theorem in ΔACE, we get
AC2 + CE2 =AE2 ………………………………………….(i)
In ΔBCD, by Pythagoras theorem, we get
BC2 + CD2 =BD2 ………………………………..(ii)
From equations (i) and (ii),we get,
AC2 + CE2 +BC2 + CD2 = AE2 +BD2 …………..(iii)
In ΔCDE, by Pythagoras theorem, we get
DE2 = CD2 +CE2
In ΔABC, by Pythagoras theorem, we get
AB2 = AC2 +CB2
Putting the above two values in equation (iii), we get
DE2 + AB2 = AE2 + BD2.