Answer:
1. Addition Property of Equality
2. Segment addition
3. Substitution Property of Equality.
4. Transitive Property of Equality.
Step-by-step explanation:
Here, given : CD = EF and AB = CE
To Show: AB = DF
Now, as given in the steps:
1. CD + DE = EF + DE by the (addition) Property of Equality.
As we have added the EQUAL QUANTITY on both sides of the equality.
2.CE = CD + DE and DF = EF + DE by (segment addition).
As here CE and DF are line segments. And the length of a
Line Segment = Sum of all its parts in which it is divided.
3.CE = DF by the (Addition, subtraction, substitution, transitive)Property of Equality.
Here, as we know CE = CD + DE
but CD = EF , so SUBSTITUTE EF in place of CD
⇒ CE = EF + ED = FD (by substitution) Property of Equality.
4.Given, AB = CE and CE = DF implies AB = DF by the (transitive)Property of Equality.
As, x = y , y = z ⇒ x = z is the TRANSITIVE PROPERTY
