Understand & Think (1pt): What is being asked in the problem below and what does that mean? What do I know and what does it mean? What plan am I going to try?
Do/Answer (2pts): I will write out my response to the question, explaining my answer and what it means. I will explain why my answer makes sense.
For question 1, use each of the reasons found in the Reasoning Bank (below), to complete the proof. (+2 pts)
Pro-tip: The reason explains how you got the statement, not what to do next.
Given: AB = 28; M lies on the line AB
Prove: M is a midpoint.
Statements
Reasons
1) M lies on AB
AB = 28
1)
2) AM + MB = AB
2)
3) 2x + 2 + 4x - 10 = 28
3) Substitution Property
4) 6x - 8 = 28
4)
5) 6x = 36
5)
6) x = 6
6)
7) AM = 2(6) + 2 and
MB = 4(6) - 10
7) Substitution Property
8) AM = 14 and MB = 14
8) Simplifying
9) M is a midpoint
9)
Reasoning Bank:
1) M lies on AB: This is given in the problem statement. It means that point M is located on the line segment AB.
2) AB = 28: This is given in the problem statement. It means that the length of line segment AB is equal to 28 units.
3) Substitution Property: This is a property that allows us to substitute the value of x into an equation or expression.
4) 6x - 8 = 28: This is the algebraic equation obtained by substituting the values of AM and MB into the equation AM + MB = AB.
5) 6x = 36: This is obtained by adding 8 to both sides of the equation in order to isolate the variable term.
6) x = 6: This is obtained by dividing both sides of the equation by 6 in order to solve for x.
7) Substitution Property: This allows us to substitute the value of x = 6 into the equations for AM and MB.
8) Simplifying: This step involves simplifying the expressions for AM and MB using the value of x = 6.
9) M is a midpoint: This is the conclusion of the proof, which states that point M is a midpoint of line segment AB.
Using the reasoning from the Reasoning Bank, we can prove that M is a midpoint.
My answer makes sense because I followed the logical steps of substituting the given values, solving the equation, and simplifying the expressions to reach the conclusion that M is a midpoint. The given information of AB = 28 and M lies on AB establishes the framework for the proof, and the algebraic manipulations lead to the final conclusion.