Question

select the correct answer from each drop - down menu.
given: ( cd = ef ), ( ab = ce )
prove: ( ab = df )
the lengths ( ce = cd + de ) and ( df = ef + de ) by segment addition. it was given that ( cd = ef ) and applying the substitution property of equality gives ( df = cd + de ). since both ( ce ) and ( df ) equal the same quantity, ( ce = df ) by the transitive property of equality. it was also given that ( ab = ce ). applying the transitive property of equality again, ( ab = df ).
use the paragraph proof to complete the two - column proof.
what statement and reason belong in line 4?

statements	reasons
2. ( cd = ef )	2. given
3. ( df = cd + de )	3. substitution property of equality
4.	4.
5.	5. given
6.	6. transitive property of equality

(the drop - down for line 4 statement has options: ( df = ce ), ( cd = de ), ( de = ef ), ( ab = cd ))

Explanation:

Step1: Match proof flow to line 4

From the paragraph proof, after $DF = CD + DE$, we use the transitive property with $CE = CD + DE$ to get $CE = DF$.

Step2: Identify correct statement/reason

The statement is $CE = DF$, and the reason is the transitive property of equality (since both $CE$ and $DF$ equal $CD+DE$).

Answer:

Statement: $CE = DF$

Reason: transitive property of equality