Question

X and Y are point of the sides AB and AC respectively of a triangle ABC such that AX/AB =1/4 , AY = 2 cm and YC = 6 cm . Find wheather XY|| BC or not

Answer 1

xy is parallel to BC because a x / a b is equals to 1 divided by 4 and a y / AC is equals to 2 / 8 that is 1 / 4 so the ratio is same then xy is parallel to BC.

Answer 2

Answer:

XY is parallel to BC

Step-by-step explanation:

Given

$\frac{Ax}{AB}=\frac{1}{4}$

$AY=2\text{ cm}$

$YC=6\text{ cm}$

$AC=AY+YC=2+6=8\text{ cm}$

The ratio between AY and AC

$\frac{AY}{AC}=\frac{2}{8}\\\\\therefore\frac{AY}{YC}=\frac{1}{4}$

As per the side splitter theorem if a line intersect the other two sides of a triangle and the line divides those two sides proportionally then the line is parallel to the third side of a triangle.

Therefore,

$XY\parallel BC$