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प्रश्न
In the given figure below, `(AD)/(AE) = (AC)/(BD)` and ∠1 = ∠2, Show that ΔBAE ∼ ΔCAD.
उत्तर
In ΔABC,
∠1 = ∠2
∴ AB = BD ......(i)
Given, `(AD)/(AE) = (AC)/(BD)`
Using equation (i), we get
`(AD)/(AE) = (AC)/(AB)` ......(ii)
In ΔBAE and ΔCAD, by equation (ii),
`(AC)/(AB) = (AD)/(AE)`
∠A = ∠A ......(Common)
∴ ΔBAE ∼ ΔCAD ......[By SAS similarity criterion]
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