Given: ad = cf bc = de prove: ab = ef statement reason 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 what is the reason for the fourth statement in this proof? a. definition of collinear points b. segment addition c. subtraction property of equality d. substitution property of equality

option C is correct.

It is Subtraction Property of Equality.

Step-by-step 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 + EFTransitive Property of Equality

4.  AB + BC = DE + EF

5.   BC = DEgiven

6. AB = EFSubtraction 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.

hello! just here for points! though i wish i knew!