Question

select the correct answer from each drop - down menu
given: ( cd = ef ), ( ab = ce )
prove: ( ab = df )
there is a diagram with two line segments. the upper segment has endpoints a and b. the lower segment has endpoints c, d, e, f in order.
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. drop - down for statement	4. drop - down for reason
5. ( ab = ce )	5. given
6. ( ab = df )	6. transitive property of equality

Explanation:

Step1: Map paragraph proof to table

From the given paragraph proof, after step 3 ($DF=CD+DE$), we establish that $CE=DF$ using the transitive property (since $CE=CD+DE$ and $DF=CD+DE$).

Step2: Identify line 4 content

This matches the missing line 4: the statement is $CE=DF$, and the reason is the transitive property of equality.

Answer:

Statement: $CE = DF$
Reason: transitive property of equality