Question

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

Answer 1

C is the correct answer according to Edmentum

Explanation:

Answer 2

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.