Question

PLEASE HELP !!! What is the next step in the given proof? Choose the most logical approach.

Answer 1

Since, it is given that AB=CE, CD=EF.

To Prove: AB = DF

Proof:

CD = EF (Given)

CD+DE = DE+EF (Addition property of Equality)

CE = CD+DE (Segment Addition)

DF = DE+EF

Since, CE = CD+DE and CD+DE = DE+EF and DE+EF = DF

So, CE = DF(Transitive Property of Equality)

Transitive property of Equality states that "If a = b and b = c, then a = c".

Answer 2

Answer:
Statement: CE=DF
Reason: Transitive property of equality

CD=EF                  -----> given
CD+ DE= EF+ DE     -----> add DE to both side

CE = CD+DE      
DF= EF+ DE     

CE=DF     -----> transitive property of equality, since CD+DE = EF+ DE 

Since CE=DF and AB=CE (given), then AB=DF