Geometry worksheet focusing on the Segment Addition Postulate with various problems to find segment lengths.

I'll solve the problems in this "Segment Addition Postulate" worksheet step by step.

Let me first look at the image to understand what's being asked and then solve each problem.

First, look closely:
The worksheet contains 10 problems related to the Segment Addition Postulate. The postulate states that if point B is between points A and C, then AB + BC = AC.

Let me start with problem 1:
- We have a line segment with points A, B, and C.
- AB = x + 4, BC = 2x - 6, and AC = 30.
- Since B is between A and C, we can use the Segment Addition Postulate: AB + BC = AC.

Let me solve this problem:

(x + 4) + (2x - 6) = 30
3x - 2 = 30
3x = 32
x = 32/3

Now let me check problem 2:
- We have a line segment with points A, B, and C.
- AB = 2x + 3, BC = 5x - 7, and AC = 30.
- Using the Segment Addition Postulate: AB + BC = AC.

(2x + 3) + (5x - 7) = 30
7x - 4 = 30
7x = 34
x = 34/7

Let me continue with problem 3:
- We have a line segment with points A, B, and C.
- AB = x, BC = 2x, and AC = 24.
- Using the Segment Addition Postulate: AB + BC = AC.

x + 2x = 24
3x = 24
x = 8

Problem 4:
- We have a line segment with points A, B, and C.
- AB = 14, BC = x, and AC = 30.
- Using the Segment Addition Postulate: AB + BC = AC.

14 + x = 30
x = 16

Problem 5:
- We need to find KL.
- We have a line segment with points K, L, and M.
- KL = 11, LM = 12, and KM = 26.
- Using the Segment Addition Postulate: KL + LM = KM.
- But we're asked to find KL, which is already given as 11. This seems to be asking for verification or perhaps there's an error in interpretation.

Actually, looking more carefully, I think problem 5 is asking us to find the length of KL given the total length KM and the length LM.
Since K, L, and M are collinear with L between K and M, we have: KL + LM = KM.
KL + 12 = 26
KL = 14

Problem 6:
- We need to find HI.
- We have a line segment with points H, I, and J.
- HI = x, IJ = 12, and HJ = 20.
- Using the Segment Addition Postulate: HI + IJ = HJ.

x + 12 = 20
x = 8

Problem 7:
- We need to find BC.
- We have a line segment with points A, B, and C.
- AB = 19, BC = x, and AC = 30.
- Using the Segment Addition Postulate: AB + BC = AC.

19 + x = 30
x = 11

Problem 8:
- We need to find HK.
- We have a line segment with points H, K, and L.
- HK = x, KL = 11, and HL = 20.
- Using the Segment Addition Postulate: HK + KL = HL.

x + 11 = 20
x = 9

Problem 9:
- Points A, B, and C are collinear. Point B is between A and C.
- We're given AB = 16 and BC = 12.
- We need to find AC.
- Using the Segment Addition Postulate: AC = AB + BC = 16 + 12 = 28.

Problem 10:
- Points A, B, and C are collinear. Point B is between A and C.
- We're given AB = 13 and BC = 9.
- We need to find AC.
- Using the Segment Addition Postulate: AC = AB + BC = 13 + 9 = 22.

Let me summarize the solutions:

1. x = 32/3
2. x = 34/7
3. x = 8
4. x = 16
5. KL = 14
6. HI = 8
7. BC = 11
8. HK = 9
9. AC = 28
10. AC = 22