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

 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.

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