In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF.

Answer:

The answer is option c.

Step-by-step explanation:

CD = EF                  -----> as given

CD + DE = EF + DE     -----> adding DE to both sides

CE = CD + DE      

DF = EF + DE     

Consequently, CE = DF      -----> due to the transitive property of equality, given that CD + DE = EF + DE 

Since CE = DF and AB = CE (as given), it follows that AB = DF.

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Given: CD = EF and AB = CE

To Show: AB = DF

Following the steps outlined:

1. CD + DE = EF + DE by the (addition) Property of Equality.

This shows that the same value has been added to both sides of the equation.

2. CE = CD + DE and DF = EF + DE through (segment addition).

This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.

3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.

So, CE = EF + ED = FD (via substitution) Property of Equality.

4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.

This follows the rule that if x = y and y = z, then x = z.