1-2 Segment Addition and Midpoint

1. 1-2 Segment Addition and Midpoint Segment Addition Postulate: If B is between A and C, then AB + BC = AC A B C

2. G R F S H T Example) G is between F and H, FG = 6, and GH = 11. Find FH. Example) R is between T and S, RT = 12, and ST = 23. Find RS. FG + GH = FH 6 + 11 = FH 17 = FH 11 6 23 SR + RT = ST SR + 12 = 23 -12 -12 SR = 11 12

3. P M S N T O Example) P is between S and T. SP = 2x + 3, PT = 3x + 2, and ST = 25. Find the length of PT. Example) M is between N and O. NM = 17, MO = 3x-5, and NO = 5x + 2. Find the length of NO. 25 SP + PT = ST (2x+3) + (3x+2) = 25 5x + 5 = 25 5x = 20 x = 4 PT = 3(4)+2 PT = 14 3x+2 2x+3 5x+2 NM + MO = NO (17) + (3x-5) = (5x-2) 3x+12 = 5x-2 12 = 2x -2 14 = 2x 7 = x NO= 5(7)+2 NO= 37 3x-5 17

4. 6 A M B 3 3 midpoint Bisect- to cut into two congruent parts. Midpoint- A point that bisects a segment (in the middle).

5. 4x+2 RT + RS = ST (12) + (12) = (4x+2) 24 = 4x+2 22 = 4x 5.5 = x R M B T X A Y C S Example) R is the midpoint of TS, RT = 12 and ST = 4x+2. Find ‘x’. Example) M is the midpoint of XY, XM= 3x+2 and YM = 5x-8. Find XY. Example) B is the midpoint of AC, BC= 6x+3 and AC = 15x – 6. Find AB. 12 XM = YM (3x+2) = (5x-8) 2 = 2x-8 10 = 2x 5 = x XM = 3(5)+2 XM = 17 XY = 34 3x+2 5x-8 AB + BC = AC (6x+3) + (6x+3) = (15x-6) 12x+6 = 15x-6 6 = 3x-6 12 = 3x 4 = x 15x-6 BC = 6(4)+3 BC = 27 AB = BC AB = 27 6x+3