Question

If a line divides any two sides of a
triangle in the same ratio, then the

line is parallel to the third side. *
True
ОО
False​

Answer 1

Answer:

TRUE...

A line joining the mid-points of any two sides of a triangle is parallel to the third side.

Complete step-by-step answer:

Let us assume a △ABC

in which D and Eare the mid points of sides AB and AC respectively.

To prove : DE||BC .

Proof :

Here , D and E are the mid points of AB and AC

And we know that midpoint bisects a side into two equal parts .

So, AD=DB .

⇒AD=DB=1 ……(i)

Similarly we have , AE=EC

⇒AE=EC=1 …...(ii)

Equating equation (i) and (ii), we get

⇒AD=DB=AE=EC .

Thus ,the line DE divides the sides AB and AC of △ABC

in the same ratio, therefore by the converse of basic proportionality theorem ,we have

⇒ DE||BC