triangles

Asked by  | 11th Jan, 2010, 10:23: PM

Expert Answer:

In rt traingle AED,

AD2 = AE2 + DE2       ...................(1)

In rt traingle AEC,

AC2 = AE2 + CE2  

        =  AE2 + (CD + DE)2  

        = AE2 + CD2 + DE2  + 2CD. DE

        = AE2 + BD2 + DE2  + 2BD. DE  .................(2)

In rt traingle AEC,

AB2 = AE2 + BE2  

        =  AE2 + (BD - DE)2  

        = AE2 + BD2 + DE2  - 2BD. DE   .................(3)

Adding equation (2) and (3), we get

AC2 + AB2 = 2AE2 + 2BD2 + 2DE2  

                   = 2 (AE2 + DE2 ) +  2BD2

Now using  equation (1), we get

 AC2 + AB2 = 2 (AD2 + BD2).

Hence the answer.

Answered by  | 12th Jan, 2010, 10:34: AM

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