For question 1, use the reasons found in the Reasoning Bank below, to complete the proof. 1. Given: AB = 64; M lies on the line AB AM=4x+4 BM=6x-10 Prove: M is a midpoint. Statements Reasons 1) M lies on AB AB = 64 1 ) 2) AM + MB = AB 2 ) segment addition postulate 3) 4x + 4 + 6x – 10 = 64 3) Substitution Property 4) 10x – 6 = 64 4 ) 5) 10x = 70 5 ) 6) x = 7 6 ) 7) AM = 4(7) + 4 and MB = 6(7) - 10 7) Substitution Property 8) AM = 32 and MB = 32 8) Simplifying 9) M is a midpoint 9 ) definition of midpoint Reasoning Bank Now that you have completed a proof by filling in the reasons for someone else’s statements (their work/steps), try to do a little bit of both on your own. You do not have to turn in your work for how you problem-solve through this proof or the next one, but you should write it out on your own to help you complete the rest of the sample work assignment. For question 2, use your GeomA Reference sheet (posted on the Message Board), to complete the proof. 2. Given: Angles 1 and 2 are a linear pair. Prove that x = 16 Statements Reasons 1) Angles 1 and 2 are a linear pair. 1) Given 2) Angles 1 and 2 are supplementary. 2) Linear Pair Postulate 3) m∠1 + m∠2 = 180° 3) 4) 10x + 1 + x + 3 = 180 4) 5) 11x + 4 = 180 5) 6) 11x = 176 6) 7) x = 16 7) For question 3, use your GeomA Reference sheet (posted on the Message Board), to complete the proof. 3. Given: 8(3x-4)=15x+40 Prove: x = 8 Statements Reasons 1 ) 1) 2) 24x-32=15x+40 2) 3 ) 3) Addition Property of Equality 4) 9x = 72 4) 5 ) 5)