Q10 of 56 Page 119

If D and E are points lying on sides AB and AC respectively of ΔABC such that BD = CE. Then prove that ΔABC is an isosceles triangle.


In ΔADE & ΔABC,


∠ADE = ∠ABC


∠A = ∠A


ΔADE~ΔABC by AA Similarity Rule



BD = CE


⇒ AD = AE


Now,


AD + BD = AE + CE


AB = AC


Thus, the triangle ABC is isosceles.


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