Question

Select the correct answer. 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

Step-by-step explanation: The answer is D- Substitution Property of Equality. I just did the test and it was right.

Answer 2

C. Subtraction property of equality.

Explanation:

Given AD= CF

And BC=DE

To prove that AB=EF

Proof:

1.Statement: AD=CF

Reason: Given in question.

2. Statement: AD= AB+BC+ CD, CF= CD+DE+EF

Reason: Segment addition property because AB,BC,and CD are the segments of AB and CD,DE and DE are segments of CF.

3. Statement: AB+BC+CD=CD+DE+EF

Reason: Transitive property of equality

Transitive property: If ab=bc and bc=ca

Then , ab=ca

4.Statement: AB+BC= DE+EF

Reason: By using subtraction property of equality.

5. Statement:BC=DE

Reason: Given in question.

6. Statement: AB=EF

Reason: when we put BC=DE . Then we get AB+DE=DE+EF. By using subtraction property of equality .

Hence proved .