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प्रश्न
In figure, ABCD is a trapezium with AB || DC. If ∆AED is similar to ∆BEC, prove that AD = BC.
योग
उत्तर
It is given that ∆AED ~ ∆BEC
`"AE"/"BE"="ED"/"EC"="AD"/"BC" ….(i)` {Corresponding sides are Proportional}
In ∆ABE and ∆CDE,
∠AEB = ∠CED [Vertically opposite angles]
∠EAB = ∠ECD [Alternate angles]
∴ ∆ABE ~ ∆CDE [AA Similarity]
`=> "AB"/"CD" = "EB"/"ED"="AE"/"EC"` {Corresponding sides are Proportional}
`"EC"/"ED" = "AE"/"EB" ….(ii)`
From (i) and (ii), we get
`"AD"/"BC"="ED"/"EC"`
`=> "AD"/"BC"=1` (ED = EC)
∴ AD = BC Proved.
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