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
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.