XY is drawn parallel to the base BC of cutting AB at X and AC at Y. If AB = 4 BX and YC = 2 cm, then AY =

Given XY is drawn parallel to the base BC of a ΔABC cutting AB at X and AC at Y. AB = 4BX and YC = 2 cm.

In ΔAXY and ΔABC,

∠AXY = ∠ABC [corresponding angles]

∠AYX = ∠ACB [corresponding angles]

∠A = ∠A [common angle]

We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

∴ ΔAXY ~ ΔABC

Let BX = x, so AB = 4x and AX = 3x.

We know that two triangles are similar if their corresponding sides are proportional.

∴ AY = 6 cm