Write a two column proof of the following : GIVEN : BC=DE PROVE:BD=CE

Question

given: BC=DE 

prove : BD=CE

Answer 1

Since you have no diagram, I am assuming that B,C,D,E are all on the same line segment.

 

The reflexive postulate states that and quantity is equal to itself.

The addition postulate states that if 2 equal quantities are added, their sums are equal.

The Substitution postulate says that if 2 quantities are equal, the can be replaced for one another in any numerical expression.

Some teachers use the partition postulate that says that the whole is equal to the sum of its parts.

 

     Statements                 Reasons

1. BC=DE                        1. given as true

2. CD=CD                        2. reflexive postulate

3. BC+CD = DE+CD         3. Addition postulate

4. BD= BC+CD

    CE=DE+CD                  4. partition postulate

5. BD=CE                        5. Substitution Postulate

 

Hope this helped