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

The correct option is: C

Step-by-step explanation:

Since we are given steps so as to prove: AB=EF

1. AD = CFgiven

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

The reason for the fourth statement in the proof is Subtraction Property of Equality.

" Since the side CD is added on both the sides of the equality; so we can subtract it from both the sides in order to obtain our statement 4 and proceed further " .

Hence option C is correct.