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match the reasons to complete the proof by using drag and drop.

Given line segment AB=28: M lies on the line AB Prove M is a midpoint.
Between A and M says 2x+2 and between m and b says 4x-10
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) ________________
Word bank:
Addition property of equality
Combine like terms
definition of a midpoint
divisions property of equality
Segment addition postulate
given

1 answer

Here is the completed proof with the appropriate reasons matched to each statement:

Statements: Reasons:

  1. M lies on AB, AB=28 1) Given
  2. AM + MB = AB 2) Segment addition postulate
  3. 2x + 2 + 4x - 10 = 28 3) Substitution Property
  4. 6x - 8 = 28 4) Combine like terms
  5. 6x = 36 5) Addition property of equality
  6. x = 6 6) Division property of equality
  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) Definition of a midpoint

This arrangement matches the statements with their corresponding reasons to complete the proof that M is a midpoint of segment AB.