Question

Draw any triangle ABC. draw line DE parallel to BC such that A-D-B and A-E-C. measure the lengths of segments AD, DB, AE, EC. verify the basic proportionality theorem​

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.