Mathematics
Grade9
Easy

Question

The steps of a proof are shown.
Given: T is the midpoint of stack S U with minus on top.
Prove: x = 5

What is reason 4?
Statements Reasons
1. T is the midpoint of Error converting from MathML to accessible text. 1. Given
2. Error converting from MathML to accessible text.  
3. ST = TU  
4. 7x = 3x + 20  
5. 4x = 20  
6. x = 5  

  1. Definition of midpoint
  2. Division Property of Equality
  3. Substitution Property of Equality
  4. Definition of congruent segments

Hint:

 

The correct answer is: Substitution Property of Equality


    The whole proof:
    Statements Reasons
    1. T is the midpoint of Error converting from MathML to accessible text. 1. Given
    2. Error converting from MathML to accessible text. 2. Definition of midpoint
    3. ST = TU 3. Definition of congruent segments
    4. 7x = 3x + 20 4. Substitution Property of Equality
    5. 4x = 20 5. Subtraction Property of Equality
    6. x = 5 6. Division Property of Equality

     In this question, we have to find the reason for 4. As congruent line segments are defined as line segments which are equal in length, the division property of equality states that dividing both sides of an equation by the same number does not affect the equation, the substitution property of equality allows equal quantities to replace each other at any time in any math sentence and a midpoint is a point on a line segment that divides it into two equal parts.

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