In the fig. AD/DB = AE/EC and angle ADE = angle ACB. Prove that ABC is an isosceles triangle.
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Step-by-step explanation:
AD/DB = AE/EC
So, DE II BC (By the converse of Thales's Theorem)
⇒ ∠ ADE = ∠ ABC ( Corresponding angles)
But, ∠ ADE = ∠ ACB (given)
So, ∠ ABC = ∠ ACB
⇒AC = AB (SIDES OPPOSITE TO EQUAL ANGLES)
Hence, ABC is an isosceles triangle.
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