Question

Given: CE = DF
Prove: CD = EF

It is given that CE = DF. By the Segment Addition Postulate, CE = CD + DE and DF = DE + EF. So, CD + DE = DE + EF by the Substitution Property of Equality.
A) Therefore, CD = EF because of the Subtraction Property of Equality.
B) Therefore, CE = DF because of the definition of congruent segments.
C) Therefore, CD + DE + EF = CF because of the Segment Addition Postulate.
D) Therefore, D is the midpoint of line segment CE because CD = DE.

Answer 1

A) Therefore, CD = EF because of the Subtraction Property of Equality

CD + DE = DE + EF

You can get rid of DE by subtracting it from both sides and this is how you’re left with
CD = EF

You can subtract it from both sides because of the subtraction property of equality