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