In triangle ABC if X and Y are points on AB and AC respectively such that AX/XB = 3/4, AY = 5 and YC = 9. Are XY and BC parallel or not?

Given that, ABC is a triangle.

X and Y are points on AB and AC.

, AY = 5 and YC = 9

To find out whether XY and BC will be parallel or not, let us assume that XY is parallel to BC.

In this case:

If XY ∥ BC,

Then obviously ∆ABC ∼ ∆AXY.

As clearly the sides AB ∥ AX, AC ∥ AY.

Also, if the triangles are the similar then the ratio of the corresponding sides will be same.

That is,

If ∆ABC ∼ ∆AXY, then

&

But, note that

So, this means that ∆ABC is not similar to ∆AXY.

⇒ XY is not parallel to BC.

Thus, by contradiction, we can say that,

XY is not parallel to BC.