Question

In the adjoining figure DX =4 , DE= 8, FY =6, DF=12 .complete the following activity to prove that seg XY || seg EF​

Answer 1

QUESTION:

• In the adjoining figure DX =4 , DE= 8, FY =6, DF=12 .complete the following activity to prove that seg XY || seg EF

GIVEN:

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

To Find :

• prove that seg XY ll seg EEF

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

As DX/XE = DY/YF = 1

=> XY || EF

• QED

Hence Proved