Mathematics

Grade9

Easy

Question

# The steps of the proof are shown.

GIVEN ⇒ 2AB = AC

PROVE: AB = BC

1. 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?

- Given
- Distributive Property
- Substitution Property
- Transitive Property

Hint:

### In this question . we have given a line A following B and C. And given is 2AB = AC and we have to prove here AB = AC. Now have to find the step 2 reason. Use property of equality.

## 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 = AC

2. 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 property

Or,

Distributive Property

The 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)

In this question, we have to find the reason of step 2. In distributive property, If this is given then A+(B+C) = (A+B)+C.