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प्रश्न
In the given figure, ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"` Prove that ΔABC is isosceles.
योग
उत्तर
Given:
∠D = ∠E
`"AD"/"BD" = "AE"/"EC"`
To Prove: ΔABC is isosceles
Proof: In ΔADE
∠D = ∠E
And, `"AD"/"BD" = "AE"/"EC"` ...(given)
∴ `"DE"/"BC"` ...(By converse of B.P.T)
In ΔABC
∠D = ∠B ...[Corresponding's are equal]
∠E = ∠C
Thus ∠B = ∠C ...(from (i))
∴ AB = AC (sides opposite to equal angles) are equal Hence, ΔABC is isosceles.
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