An important question from similarity chapter in which we have been asked to prove that triangle ABC is an isosceles if DE∥BC and BD=CE
ML Aggarwal Avichal Publication Similarity, chapter 13.2, question no 5a
Rajan@2021Guru
In figure (i) given below, DE∥BC and BD=CE. Prove that ABC is an isosceles triangle.
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From the question it is given that,
DE∥BC and BD=CE
So, we have to prove that ABC is an isosceles triangle.
Consider the triangle ABC,
AD/DB=AE/EC
Given, DB=EC … [equation (i)]
Then, AD=AE … [equation (ii)]
By adding equation (i) and equation (ii) we get,
AD+DB=AE+EC
So, AB=AC
Therefore, △ABC is an isosceles triangle