1) Given
2) Definition of Midpoint (M is the point that divides AB into two equal segments, AM and MB)
3) Substitution Property (replace AB with 28)
4) Combine like terms (-10 + 2 = -8)
5) Addition Property of Equality (add -8 to both sides of the equation)
6) Division Property of Equality (divide both sides by 6)
7) Substitution Property (replace x with 6)
8) Simplifying (2(6) + 2 = 14 and 4(6) - 10 = 14)
9) Definition of Midpoint (AM and MB have equal lengths and M is the point that divides AB into two equal segments)
Based on the given information and the steps in the proof, we can conclude that M is a midpoint because it satisfies the definition of a midpoint - it divides the line AB into two equal segments. Additionally, the calculations in steps 7 and 8 show that the lengths of AM and MB are both 14, further supporting the fact that M is a midpoint. Therefore, my answer makes sense because it is supported by the given information and the logical progression of the proof.
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:
Addition Property of Equality, Combine like terms, Definition of Midpoint, Division Property of Equality, Given, and Segment Addition Postulate
5 answers
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)
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)
To complete the proof, we can use the information given and the properties from the GeomA Reference sheet.
1) Given
2) Linear Pair Postulate (Angles that form a linear pair are supplementary)
3) Definition of supplementary angles (m∠1 + m∠2 = 180°)
4) Simplifying the expression (11x - 6 + 4x + 21 = 180)
5) Combine like terms (15x + 15 = 180)
6) Isolate the variable (15x = 165)
7) Solve for x (x = 11)
Based on the given information and the steps in the proof, we can conclude that x = 11. This means that the value of x that satisfies the given conditions is 11. This conclusion aligns with the calculations and properties used in the proof. Therefore, my answer makes sense because it is supported by the given information and the logical progression of the proof.
1) Given
2) Linear Pair Postulate (Angles that form a linear pair are supplementary)
3) Definition of supplementary angles (m∠1 + m∠2 = 180°)
4) Simplifying the expression (11x - 6 + 4x + 21 = 180)
5) Combine like terms (15x + 15 = 180)
6) Isolate the variable (15x = 165)
7) Solve for x (x = 11)
Based on the given information and the steps in the proof, we can conclude that x = 11. This means that the value of x that satisfies the given conditions is 11. This conclusion aligns with the calculations and properties used in the proof. Therefore, my answer makes sense because it is supported by the given information and the logical progression of the proof.
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
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
To complete the proof, we need to solve the equation -2(x - 4) = 2x + 12 and show that it leads to the conclusion x = -1.
1) Given
2) Distributive Property (-2 * x = -2x and -2 * -4 = 8)
3) Simplifying the expression (-2x + 8 = 2x + 12)
4) Combining like terms (subtracting 2x from both sides, we get -4x + 8 = 12)
5) Subtracting 8 from both sides (we get -4x = 4)
6) Division Property of Equality (dividing both sides by -4, we get x = -1)
Based on the given equation and the steps in the proof, we can conclude that x = -1. This means that when we solve the equation -2(x - 4) = 2x + 12, the value of x that satisfies the equation is -1. This conclusion aligns with the calculations and properties used in the proof. Therefore, my answer makes sense because it is supported by the given information and the logical progression of the proof.
1) Given
2) Distributive Property (-2 * x = -2x and -2 * -4 = 8)
3) Simplifying the expression (-2x + 8 = 2x + 12)
4) Combining like terms (subtracting 2x from both sides, we get -4x + 8 = 12)
5) Subtracting 8 from both sides (we get -4x = 4)
6) Division Property of Equality (dividing both sides by -4, we get x = -1)
Based on the given equation and the steps in the proof, we can conclude that x = -1. This means that when we solve the equation -2(x - 4) = 2x + 12, the value of x that satisfies the equation is -1. This conclusion aligns with the calculations and properties used in the proof. Therefore, my answer makes sense because it is supported by the given information and the logical progression of the proof.