Answer:
option C is correct.
It is Subtraction Property of Equality.
Explanation:
Since, we are given the following statements for a proof:
1. AD =CF------- given
2. AD = AB + BC + CD CF = CD + DE + EF------- segment addition
3. AB + BC + CD = CD + DE + EF-----------Transitive Property of Equality
4. AB + BC = DE + EF
5. BC = DE------- given
6. AB = EF---------- Subtraction Property of Equality
As in third step we are given:
AB + BC + CD = CD + DE + EF
and going to the fourth step we are left with the term:
AB + BC = DE + EF
This means we are using subtraction property of equality.
" Since, CD term is same on both the sides of the equality so we subtract it from both the sides so as to get step fourth and proceed further for the proof ".
Hence, option C is correct.