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?

  1. Given
  2. Distributive Property
  3. Substitution Property
  4. 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.

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