Question

From this given statement, select the definition , property, postulate, or theorem that justifies the prove statement.

Given: AD = DB and CD = DE
Prove: AD + CD = DE + DE

A: definition of a segment bisector
B: Multiplication Property
C: Substitution Property
D: Addition Property
E: Reflexive Property

Answer 1

The Addition Property justifies the given prove statement that AD + CD = DE + DE.

Step-by-step explanation:

The property that justifies the given prove statement is the Addition Property.

This property states that if two quantities are equal, then adding the same value to both sides of an equation will still result in two equal quantities.

In this case, since we are given that AD = DB and CD = DE, we can use the Addition Property to add AD and CD to both sides of the equation to prove that AD + CD = DE + DE.

Answer 2

Additive property of equality states that:

if a=b, then a+c = b+c,

that is, if 2 quantities of the same value are added the same quantity, they are again equal.


In our problem a=AD, b=DB, and c= CD=DE

thus a+c=b+c means AD + CD = DE + DE,

by the Addition Property


Answer: Addition Property