**Solution:** In ∆ ACE; AE^{2} = AC^{2} + CE^{2} ……… (1)

In ∆ DCB; BD^{2} = DC^{2} + CB^{2} ……… (2)

In ∆ ACB; AB^{2} = AC^{2} + CB^{2} ……… (3)

In ∆ DCE; DE^{2} = DC^{2} + CE^{2} ……… (4)

Adding equations (1) and (2), we get;

AE^{2} + BD^{2} = AC^{2} + CE^{2} + DC^{2} + CB^{2} …….. (5)

Adding equations (3) and (4), we get;

AB^{2} + DE^{2} = AC^{2} + CB^{2} + DC^{2} + CE^{2} ………. (6)

On comparing the RHS of equations (5) and(6), we get;

AE^{2} + BD^{2} = AB^{2} + DE^{2} proved