Answer:
1. Addition Property of Equality
2. Segment addition
3. Substitution Property of Equality.
4. Transitive Property of Equality.
Step-by-step explanation:
Given: CD = EF and AB = CE
To Show: AB = DF
Following the steps outlined:
1. CD + DE = EF + DE by the (addition) Property of Equality.
This shows that the same value has been added to both sides of the equation.
2. CE = CD + DE and DF = EF + DE through (segment addition).
This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.
3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.
So, CE = EF + ED = FD (via substitution) Property of Equality.
4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.
This follows the rule that if x = y and y = z, then x = z.
