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) This is given in the problem statement. It means that point M is located on the line segment AB.
2) AM + MB = AB
2) This is given in the problem statement. It means that the length of line segment AB is equal to 28 units.
3) 2x + 2 + 4x - 10 = 28
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
4) This is the algebraic equation obtained by substituting the values of AM and MB into the equation AM + MB = AB.
5) 6x = 36
5) This is obtained by adding 8 to both sides of the equation in order to isolate the variable term.
6) x = 6
6) This is obtained by dividing both sides of the equation by 6 in order to solve for x.
7) AM = 2(6) + 2 and
MB = 4(6) - 10
7) Substitution Property
This allows us to substitute the value of x = 6 into the equations for AM and MB.
8) AM = 14 and MB = 14
8) Simplifying
This step involves simplifying the expressions for AM and MB using the value of x = 6.
9) M is a midpoint
9) This is the conclusion of the proof, which states that point M is a midpoint of line segment AB.
Reasoning Bank:
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.
Now that you have completed a proof by filling in the reasons for someone else’s statements (their work/steps), try to do a little bit of both on your own. For question 2, use your GeomA Reference sheet (posted on the Message Board/padlet), to complete the proof. (2pts)
Pro-tip: What do the two expressions make?
Given: Angles 1 and 2 are a linear pair.
Prove that x = 11
Statements
Reasons
1) Angles 1 and 2 are a linear pair.
1) Given
2) Angles 1 and 2 are supplementary.
2) Linear Pair Postulate
3) m∠1 + m∠2 = 180°
3)
4) 11x - 6 + 4x + 21 = 180
4)
5) 15x + 15 = 180
5)
6) 15x = 165
6)
7) x = 11
7)
For question 2, the problem is asking to prove that x = 11. This means that we need to show that the value of x is equal to 11 based on the given information.
I know that angles 1 and 2 are a linear pair, which means that they are adjacent angles that form a straight line. This implies that the sum of their measures is 180 degrees.
To prove that x = 11, I will use the Linear Pair Postulate to show that angles 1 and 2 are supplementary. Then, I will use the fact that the sum of their measures is 180 degrees and solve for x.
1) Angles 1 and 2 are a linear pair. (Given)
2) Angles 1 and 2 are supplementary. (Linear Pair Postulate)
3) m∠1 + m∠2 = 180°. (Definition of supplementary angles)
4) 11x - 6 + 4x + 21 = 180. (Substituting the expressions for the measures of angles 1 and 2)
5) 15x + 15 = 180. (Combining like terms)
6) 15x = 165. (Subtracting 15 from both sides)
7) x = 11. (Dividing both sides by 15)
By solving the equation, I have shown that x is equal to 11. This proves the statement that was asked to be proven.