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)
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 (3pts): 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 3, use your GeomA Reference sheet (posted on the Message Board/padlet ), to complete the proof(3 pts).
Pro-tip: Solve the problem first
Given: -2(x - 4) = 2x + 12
Prove: x = -1
Statements
Reasons
1)
1)
2
2) Distributive Property
3)
3)
4) -4x = 4
4)
5)
5) Division Property of Equality
Understand & Think (1pt): The problem is asking us to prove a statement using the given information. We are given a linear pair of angles and we need to prove that a certain value of x is equal to 11. The plan is to use the properties and postulates from the Geometry Reference sheet to fill in the statements and reasons in the proof.
Do/Answer (2pts):
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) Definition of supplementary angles
4) 11x - 6 + 4x + 21 = 180
4) Substitution Property
5) 15x + 15 = 180
5) Combining like terms
6) 15x = 165
6) Subtraction Property of Equality
7) x = 11
7) Division Property of Equality
Explanation: The given information states that angles 1 and 2 form a linear pair, which means that they are adjacent and their measures sum up to 180°. Using this, we can write the equation m∠1 + m∠2 = 180°. Then, we substitute the measures of angles 1 and 2, which are 11x - 6 and 4x + 21 respectively, and set the equation equal to 180. Simplifying and solving for x, we find that x is equal to 11. This makes sense because it satisfies the given equation and proves that the statement x = 11 is true.