Question

In triangle abc x and y are the points on the sides AB and AC respectively such that AB= 2.56cm, AC= 5.12 cm, and AX= 0.32cm and AY= 0.64cm. Is XY||BC ?​

Answer 1

Step-by-step explanation:

BX = AB - AX = 2.56 - 0.32

BX = 2.24 cm

CY = AC - AY = 5.12- 0.64

CY = 4.48 cm

Now,

AX/BX - 0.32/2.24 = 32/224 = 1/7--------> ( 1 )

Also, AY/CY = 0.64/4.48 = 64/448 = 1/7--------> ( 2 )

So from ( 1 ) & ( 2 )

AX/BX = AY/CY

By the converse of "The Basic Proportionality Theorem"

AX/BX = AY/CY <=> XY || BC

Answer : Hence XY || BC