Match the reasons to complete the proof. Given: AB = 28; M lies on the line AB Prove: M is a midpoint.

Question

1) M lies on AB AB = 28 _____ . 2) AM + MB = AB _____. 3) 2x + 2 + 4x - 10 = 28 _____. 4) 6x - 8 = 28_____. 5) 6x = 36 _____. 6) x = 6 _____. 7) AM = 2(6) + 2 and MB = 4(6) - 10 _____. 8) AM = 14 and MB = 14 _____. 9) M is a midpoint _____

Answer 1

Let's match the reasons to complete the proof step-by-step based on the given statements:

1. M lies on AB. (Given)
2. AM + MB = AB. (Definition of segment addition)
3. 2x + 2 + 4x - 10 = 28. (Substitution of expressions for AM and MB in terms of x)
4. 6x - 8 = 28. (Combining like terms)
5. 6x = 36. (Adding 8 to both sides)
6. x = 6. (Dividing by 6)
7. AM = 2(6) + 2 and MB = 4(6) - 10. (Substituting x back into the expressions for AM and MB)
8. AM = 14 and MB = 14. (Calculating values from the previous step)
9. M is a midpoint. (Definition of a midpoint, since AM = MB)

So the completed proof looks like this:

1. M lies on AB. (Given)
2. AM + MB = AB. (Definition of segment addition)
3. 2x + 2 + 4x - 10 = 28. (Substitution of expressions for AM and MB in terms of x)
4. 6x - 8 = 28. (Combining like terms)
5. 6x = 36. (Adding 8 to both sides)
6. x = 6. (Dividing by 6)
7. AM = 2(6) + 2 and MB = 4(6) - 10. (Substituting x back into the expressions for AM and MB)
8. AM = 14 and MB = 14. (Calculating values from the previous step)
9. M is a midpoint. (Definition of a midpoint, since AM = MB)

Answer 2

Here are the options you can use to fill in the blanks, addition property of equality, combine like terms, substitution property, substitution property, definition of midpoint, division property of equality, segment addition postulate, simplifying, given.

Answer 3

Using the provided options, here is how to fill in the blanks for the proof:

1. M lies on AB. (Given)
2. AM + MB = AB. (Segment addition postulate)
3. 2x + 2 + 4x - 10 = 28. (Substitution property)
4. 6x - 8 = 28. (Combine like terms)
5. 6x = 36. (Addition property of equality)
6. x = 6. (Division property of equality)
7. AM = 2(6) + 2 and MB = 4(6) - 10. (Substitution property)
8. AM = 14 and MB = 14. (Simplifying)
9. M is a midpoint. (Definition of midpoint)

So the completed proof looks as follows:

1. M lies on AB. (Given)
2. AM + MB = AB. (Segment addition postulate)
3. 2x + 2 + 4x - 10 = 28. (Substitution property)
4. 6x - 8 = 28. (Combine like terms)
5. 6x = 36. (Addition property of equality)
6. x = 6. (Division property of equality)
7. AM = 2(6) + 2 and MB = 4(6) - 10. (Substitution property)
8. AM = 14 and MB = 14. (Simplifying)
9. M is a midpoint. (Definition of midpoint)

This corresponds logically to the proof steps outlined.