Mathematics
Easy

Question

# The steps of the proof are shown.GIVEN ⇒ 2AB = ACPROVE: AB = BC1. 2AB = AC (Given)2. AB + AB = AC (____)3. AB + BC = AC (Segment Addition Postulate)4. AB + AB = AB + BC (____)5. AB = BC (Subtraction Property)What is the reason for step 2?

Hint:

## The correct answer is: Distributive Property

### Here, we have to find the steps 2 reason.Firstly, given a line A following B and C and 2AB = AC .Now ,1. 2AB = AC2. AB + AB = AC ( Distributive property)3. AB + BC = AC (Segment Addition Postulate)4. AB + AB = AB + BC (Substitution property )5. AB = BC ( subtraction property)Therefore , the reason of step 2 is distributive property.The correct answer is Distributive propertyOr,Distributive PropertyThe whole proof:2AB = AC (Given)AB + AB = AC (Distributive Property)AB + BC = AC (Segment Addition Postulate)AB + AB = AB + BC (Substitution Property)AB = BC (Subtraction Property)

Distributive Property: A crucial mathematical property that will help you solve many algebraic problems is the distributive property.
The distributive property, also used as the distributive property of multiplication, demonstrates how to solve particular algebraic statements that combine addition and multiplication. For example, a number multiplied by a sum has the same effect as doing each multiplication separately, according to the literal definition of the distributive property.
The distributive property appears in an equation: a(b+c)=ab+ac. The substitution property of equality, if two variables are equal, x and y, respectively, then x can be used in place of y in any equation or expression, and 'y' can is used in place of x.