In the figure, CD = EF and AB = CE
To prove that AB = DF:
Step 1:
Given CD = EF, so we can substitute EF instead of CD.
CD + DE = EF + DE
by the Substitution Property of Equality.
Here, Option C is the correct answer.
Step 2:
CD + DE = CE and
EF + DE = DF
by Segment Addition.
Here, Option C is the correct answer.
Step 3:
From step 1, CD + DE = EF + DE
From step 2, CE = DF
So, CE = DF by the Transitive Property of Equality.
Here, Option D is the correct answer.
Step 4:
Given AB = CE and CE = DF
⇒ AB = DF
by the Transitive Property of Equality.
Here, Option D is the correct answer.
Hence proved.
