Question

In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF.

CD + DE = EF + DE by the (addition, subtraction, substitution, transitive) Property of Equality.

CE = CD + DE and DF = EF + DE by (addition, subtraction, segment addition, transitive).

CE = DF by the (Addition, subtraction, substitution, transitive)Property of Equality.

Given, AB = CE and CE = DF implies AB = DF by the (addition, subtraction, substitution, transitive)Property of Equality.

Answer 1

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

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

Answer 2

answers is c

Explanation:

CD=EF -----> given

CD+ DE= EF+ DE -----> add DE to both side

CE = CD+DE

DF= EF+ DE

CE=DF -----> transitive property of equality, since CD+DE = EF+ DE

Since CE=DF and AB=CE (given), then AB=DF