Question

Complete the proof by filling in the missing reasons using the Reasoning bank.

1. Given AB=16; M lies on the line AB
2x-2 Prove: M is a midpoint
A
4x-4
M
B
Statements Reasons
1) M lies on AB
1)
2) AM + MB = AB
2)
3)2x+2+4x-4=16
3)
4)6x-2=16
4)
5)6x=18
5)
6)x=3
6)
7)AM=2(3)+2 and MB=4(3)-4
?
?
?
?
? 7)substitution property of equality
8)AM=8 and MB=8
8)
9)M is a midpoint
9)?
Reasoning bank
Addition Property of equality Combine like terms Definition of midpoint Division property of equality Given segment Addition Postulate

Answer 1

Statements Reasons

1. M lies on AB Given

2. AM+MB=AB Definition of midpoint

3. 2x+2+4x-4 = 16 Segment Addition Postulate

4. 6x-2 = 16 Combining like terms

5. 6x = 18 Addition Property of equality

6. x = 3 Division Property of equality

7. AM=2(3)+2 and MB=4(3)-4 Substitution property of equality

8. AM=8 and MB=8 Definition of midpoint

9. M is a midpoint Hence, proved.