Question

R and S are points on the sides DE and EF respectively of a triangleDEF such that ER=5cm, RD=2.5cm, SD=1.5cm and FS=3.5cm. then find whether RS is parallel
to DF

Answer 1

we have a triangle DEF such that RS is parallel to EF ( basic proportionality theorem)
∴ DR/RE= DS/SF
 BUT
DR/RE= 2.5/5.......(i)
DS/SF=1.5/3.5......(ii)

From (i) and (ii)
DR/RE≠DS/SF
  ∴RS IS NOT parallel to EF

Answer 2

Answer:

RS is parallel  not parallel to DF.

Step-by-step explanation:

Given:

Triangle ADF

ER = 5 cm, RD = 2.5 cm, SE = 1.5 cm and FS = 3.5 cm

Construction:

Join RS

To Find:

RS is parallel to DF or not

Proof:

We have

RE = 5 cm and RD = 2.5 cm

Now,

RE / RD = 5 / 2.5

= 2 / 1

Similarly we have:

ES = 1.5 cm

SF = 3.5 cm

SF / ES = 3.5 / 1.5 = 7 / 3

Here RE / RD is not equal to SF / ES

Therefore, by the converse of Basic Proportionality Theorem we can say that RS is not parallel to DF because to be parallel RE / RD should be equal to SF / ES.