CBSE Class 10 Answered
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Asked by garimasingh | 14 Oct, 2009, 12:13: PM
Expert Answer
It is given that triangle AED is similar to triangle BEC.
To prove: AD = BC
Proof: We know that the diagonals of trapezium cut each other in same ratio.
The above stament can also be proved by showing AEB CED (AA corollary)
We get, EB/ DE = EA/ EC
Therefore, EB.EC = EA.ED ............(1)
Now, ΔAED ΔBEC
We get, AE/ BE = ED/ EC
EA. EC = EB. ED ............(2)
EB = EA
⇒ ED = EC
i.e ΔAED ΔBEC
So, AD = BC
Answered by | 22 Oct, 2009, 04:12: PM
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