Question

1. In the following figure, XY is parallel to BC,
AX = 9 cm, XB = 4.5 cm and BC = 18 cm
Find :
1. AY/YC

(ii)
YC/AC


(iii) XY​

Answer 1

ANSWER

In △AXY and △ABC

∠XAY=∠BAC (Common angle)

∠AXY=∠ABC (Corresponding angles for parallel lines XY and BC)

∠AYX=∠ACB (Corresponding angles for parallel lines XY and BC)

Thus, △AXY∼△ABC (AAA rule)

Hence, AXAB=AYAC=XYBC (Corresponding sides)

99+4.5=XY18

XY=13.518×9

XY=12cm