in the figure, cd=ef and ab= ce. complete the statements to prove that ab = df.

cd + de= ef+ de by the (addition, subtraction, substitution, or transitive)
property of equality.

ce=cd + de and df = ef + de by (addition, subtraction, segment addition, or transitive)

ce = df by the (addition, subtraction, segment addition, or transitive) property of equality.

given, ab = ce and ce = df implies ab = df by the (addition, subtraction, segment addition, or transitive) property of equality.

Hence Proved AB = DF

Step-by-step explanation:

In the Figure:

Given;

CD = EF

AB = CE

We need to prove AB = DF

Solution:

CD = EF    ⇒ (Given)

Now Adding both side by DE we get;

CD + DE = EF + DE   ⇒by the (Addition) Property of Equality.

CE=CD + DE and DF = EF + DE ⇒(Segment Addition)

Now we know that if

CE = DF           ⇒by the (transitive) Property of Equality.

Now Given:

AB = CE

CE = DF

Now we know that if

AB  = DF    ⇒by the (Transitive) Property of Equality)

The correct options to fill in the gaps are:

From the diagram given, we have that;

We are to show that the segment AB is congruent to DF

Also from the diagram

Similarly, given that:

AB = CE and CE = DF implies AB = DF by the Transitive Property of Equality.

Learn more here: link