Question
Part A: MUST SHOW ALL WORK FOR CRBDIT: (10 pens Total
Underssand & Tidak (Lp: What is being osked in the probler below and whor dues that mean? wihat da I know and what does it mean? What plan am I asia to tv?
Whac's any and rosi?.
What connections can make here? What tools.
Dalksawer (as: I will write out ay respanse to the question, explainico my answer and whar it means. fu exclain why my answer makes sense.
Aro-dia: The reason explains how you cot the statement, not what to do next.
2x42
4r a 10.
1.
B
Given: AB = 28; M lies on the line AB
Prove: M is a midpoint.
Statements
111 M lies on AB
E-08
2 A01-11B = AB
(3) 24 4 2 + 43 - 10 - 28
162-8=28
562=36
6) х = 6
7) AM = 2(6] + 2 and
(MB = 4(6) - 10
8) AM = 14 and MB = 14
9) M is a midpoint
M
Reasons
111
21
37 3mb-riE2n Propersy
41
51
巴
(7) Substitution Property
8) Simplifying
191
Reasoning Bask:
•
•
Addition Pragedy of Engality
gombina Like Lares
Defiratias, of Midpoint
.
谢
Division Propert of Equalitar
Given
Segment Addition Postulate
Underssand & Tidak (Lp: What is being osked in the probler below and whor dues that mean? wihat da I know and what does it mean? What plan am I asia to tv?
Whac's any and rosi?.
What connections can make here? What tools.
Dalksawer (as: I will write out ay respanse to the question, explainico my answer and whar it means. fu exclain why my answer makes sense.
Aro-dia: The reason explains how you cot the statement, not what to do next.
2x42
4r a 10.
1.
B
Given: AB = 28; M lies on the line AB
Prove: M is a midpoint.
Statements
111 M lies on AB
E-08
2 A01-11B = AB
(3) 24 4 2 + 43 - 10 - 28
162-8=28
562=36
6) х = 6
7) AM = 2(6] + 2 and
(MB = 4(6) - 10
8) AM = 14 and MB = 14
9) M is a midpoint
M
Reasons
111
21
37 3mb-riE2n Propersy
41
51
巴
(7) Substitution Property
8) Simplifying
191
Reasoning Bask:
•
•
Addition Pragedy of Engality
gombina Like Lares
Defiratias, of Midpoint
.
谢
Division Propert of Equalitar
Given
Segment Addition Postulate
Answers
GPT 3.5
Proof:
1. Given: AB = 28; M lies on the line AB
2. M lies on AB (Given)
3. A + MB = AB (Segment Addition Postulate)
4. 2 * AM + 2 = AB (Substitution Property)
5. 2 * AM + 2 = 28 (Substitution of AB = 28)
6. 2 * AM = 28 - 2 (Subtraction Property)
7. 2 * AM = 26 (Simplifying)
8. AM = 26 / 2 (Division Property)
9. AM = 13 (Simplifying)
10. MB = AB - AM (Segment Addition Postulate)
11. MB = 28 - 13 (Substitution of AB = 28 and AM = 13)
12. MB = 15 (Simplifying)
Therefore, we have proven that AM = 13 and MB = 15. Since AM = MB, we can conclude that M is the midpoint of AB.
Reasoning:
- In step 3, we use the Segment Addition Postulate which states that if M lies on AB, then the lengths of AM and MB added together equal the length of AB.
- In step 4, we substitute AB with 28.
- In step 7, we simplify the equation to solve for AM.
- In step 8, we divide both sides of the equation by 2 to solve for AM.
- In step 10, we use the Segment Addition Postulate again to find the length of MB.
- In step 12, we simplify the equation to find that MB = 15.
- Since AM = MB, we can conclude that M is the midpoint of AB.
1. Given: AB = 28; M lies on the line AB
2. M lies on AB (Given)
3. A + MB = AB (Segment Addition Postulate)
4. 2 * AM + 2 = AB (Substitution Property)
5. 2 * AM + 2 = 28 (Substitution of AB = 28)
6. 2 * AM = 28 - 2 (Subtraction Property)
7. 2 * AM = 26 (Simplifying)
8. AM = 26 / 2 (Division Property)
9. AM = 13 (Simplifying)
10. MB = AB - AM (Segment Addition Postulate)
11. MB = 28 - 13 (Substitution of AB = 28 and AM = 13)
12. MB = 15 (Simplifying)
Therefore, we have proven that AM = 13 and MB = 15. Since AM = MB, we can conclude that M is the midpoint of AB.
Reasoning:
- In step 3, we use the Segment Addition Postulate which states that if M lies on AB, then the lengths of AM and MB added together equal the length of AB.
- In step 4, we substitute AB with 28.
- In step 7, we simplify the equation to solve for AM.
- In step 8, we divide both sides of the equation by 2 to solve for AM.
- In step 10, we use the Segment Addition Postulate again to find the length of MB.
- In step 12, we simplify the equation to find that MB = 15.
- Since AM = MB, we can conclude that M is the midpoint of AB.