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If D and E are the points on sides AB and AC respectively of a ΔABC such that DE ∥ BC and BD = CE. Prove that ΔABC is isosceles.

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Question extracted from RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions. And has been asked in several times in exams.

In this question we have been given that D and E are the points on sides AB and AC respectively of a ΔABC

such that DE ∥ BC and BD = CE.

Now we have to Prove that ΔABC is isosceles.

 

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RD sharma, DHANPAT RAI publication

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1 Answer

  1. In Δ ABC, DE ∥ BC and BD = CE.

    To prove: that Δ ABC is isosceles.

    According to Thales Theorem,

    AD/DB = AE/EC

    But BD = CE      (Given)

    Therefore, we get,AD = AE

    Now, BD = CE and AD = AE.

    So, AD + BD = AE + CE.

    Therefore, AB = AC.

    Therefore, ΔABC is isosceles.

    Hence proved

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