Question

In the adjoining figure, DX=4,DE=8,FY=6,OF=12.complete the followiing activity to prove that seg XY ||segEf.

Answer 1

Given :  DX = 4, DE = 8, FY = 6, DF = 12.

To Find : prove that seg XY ll seg EF.​

Solution:

DX = 4, DE = 8, FY = 6, DF = 12.

DY = DF - FY = 12 - 6  = 6 cm

XE = DE - DX  = 8 - 4 = 4 cm

DX/XE  = 4/4 = 1

DY/YF  =  6/6 = 1

DX/XE = DY/YF = 1

Thale's theorem / BPT

if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

Converse is also True

if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side this is a ​ Converse of Basic Proportionality theorem or Converse of Thales Theorem

As DX/XE = DY/YF = 1

=> XY ||  EF

QED

Hence Proved

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Answer 2

easy answer send karo..