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 parallelto DF

Answer 1

Perhaps the given value is SE = 1.5 cm  and not  SD=1.5cm

In the diagram,  EF = SE + FS  = 1.5 + 3.5 = 5 cm
                          ED = ER + RD = 5 + 2.5 = 7.5 cm

Checking the ratios of corresponding sides ER & ED ; ES & EF , as they are pairs of parallel sides and the angle ∠E is common.

ES / EF = 1.5 / 5 = 0.3              
ER / ED = 5 / 7.5 = 2/3
As the ratios are not equal, the triangles are not similar.  RS is not parallel to DF.

Answer 2

RS is not parallel to DF

Step-by-step explanation:

Given:

Figure is in the attachment provided below.

RE = 5 cm

RD = 2.5 cm

DS = 1.5 cm

SF = 3.5 cm

Construction: Join RS

To check that: RF ║ DF or not

$\frac{RE}{RD}=\frac{5}{2.5}=\frac{2}{1}$

$\frac{SF}{ES} = \frac{3.5}{1.5} = \frac{7}{3}$

Here we see that,  

$\frac{RE}{RD} \neq \frac{SF}{ES}$

Therefore, RS is not parallel to DF.