Question

5-If the point D and E are situated on the sides AB and AC respectively in a triangle ABC. Such that
BC = CE, then prove that ∆ABC is an isosceles triangle .
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Answer 1

Answer:

By basic proportionality property,

⇒  DBAD=ECAE

By adding 1 on both sides,

⇒  DBAD+1=ECAE+1

⇒  DBAD+DB=ECAE+EC

⇒  DBAB=CEAC

It is given that, DE∥BC and  BD=EC

⇒  BDAB=BDAC              [ CE=BD ]

⇒  AB=AC

∴  △ABC is isosceles triangle.