CBSE Class 10 Answered
triangles
Asked by | 11 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.
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