Question

In a triangle ABC, line DE is drawn parallel to side BC such that AD/DB = AE/EC. Show that BAC is an isosceles triangle. (3 marks)

Answer 1

Given: A triangle ABC, line DE is drawn parallel to side BC such that  .  One more condition should be there that is .  To prove: Triangle ABC is isosceles triangle.  Proof: Since, line DE is parallel to BC.  By Basic Proportionality theorem,    Now, since line DE is parallel to BC.   (Corresponding angles)  (Equation 1)  Since it is given that         (Equation 2)  Therefore, by equations 1 and 2,    Therefore, AB = AC  (Because sides opposite to the equal opposite angles are equal).  Hence, triangle ABC is an isosceles triangle.