This comprehensive worksheet guides students through the Segment Addition Postulate with fill-in-the-blank notes and varied practice problems.

Let's solve each part of this Segment Addition Postulate worksheet step by step.

---

🔹 Segment Addition Postulate (Fill in the blank):

> If 3 points are ________, (on the same line segment), and B is between A and C, then ________.

✔ Answer:
- If 3 points are collinear, and B is between A and C, then
→ AB + BC = AC

This is the Segment Addition Postulate: When point B lies between points A and C on a line segment, the sum of the lengths of AB and BC equals the length of AC.

---

## ✔ Examples:

---

1. If DF = 10 and DE = 7, what is the length of EF?

We are given:
- DF = 10
- DE = 7
- Points D, E, F are collinear with E between D and F.

Using the Segment Addition Postulate:
$$
DE + EF = DF
$$
$$
7 + EF = 10
$$
$$
EF = 10 - 7 = 3
$$

✔ Answer: EF = 3

---

2. If MO = 32, find the value of x.

Given:
- MN = 2x
- NO = 3x + 7
- MO = MN + NO = 32

So:
$$
MN + NO = MO
$$
$$
2x + (3x + 7) = 32
$$
$$
5x + 7 = 32
$$
$$
5x = 25
$$
$$
x = 5
$$

✔ Answer: x = 5

---

3. If RU = 59, find TR.

Given:
- RS = 7
- ST = 3x - 4
- TU = 4x
- RU = RS + ST + TU = 59

So:
$$
RS + ST + TU = RU
$$
$$
7 + (3x - 4) + 4x = 59
$$
$$
7 + 3x - 4 + 4x = 59
$$
$$
(3x + 4x) + (7 - 4) = 59
$$
$$
7x + 3 = 59
$$
$$
7x = 56
$$
$$
x = 8
$$

Now find TR. Note that TR = TS + SR?

Wait — look at the diagram:
Points are R → S → T → U
So TR is from T to R → that’s TS + SR?

But TR means from T to R, which goes backward.

But usually we take positive direction.

But let’s clarify: TR is the segment from T to R.

But since R–S–T–U, then TR = TS + SR?

Wait: Actually, TR = RS + ST, but in reverse.

But distance is always positive.

So:
- RS = 7
- ST = 3x - 4 = 3(8) - 4 = 24 - 4 = 20

So:
$$
TR = RS + ST = 7 + 20 = 27
$$

✔ Answer: TR = 27

---

4. Solve for x. Then find the length of each segment.

We have three segments:
- First: x
- Second: x + 15
- Third: 3x
- Total: 10x + 5

From the diagram, these three segments make up the total length:
$$
x + (x + 15) + 3x = 10x + 5
$$

Left side:
$$
x + x + 15 + 3x = 5x + 15
$$

Set equal:
$$
5x + 15 = 10x + 5
$$

Subtract 5x from both sides:
$$
15 = 5x + 5
$$

Subtract 5:
$$
10 = 5x \Rightarrow x = 2
$$

Now find each segment:

- First: x = 2
- Second: x + 15 = 2 + 15 = 17
- Third: 3x = 3(2) = 6

Check total: 2 + 17 + 6 = 25
Total given: 10x + 5 = 10(2) + 5 = 20 + 5 = 25 ✔

✔ Answer:
- x = 2
- Segments: 2, 17, 6

---

5. Complete the proof.

Given: JK = MN
Prove: MN + KL = JL

Diagram: J — K — L (on one line)
And M — N (separate segment)

We’re told JK = MN.

We need to prove: MN + KL = JL

But notice: On the line J-K-L, by the Segment Addition Postulate:
$$
JK + KL = JL
$$

Since JK = MN (given), we can substitute:
$$
MN + KL = JL
$$

Now fill in the table:

| Statements | Reasons |
|-----------|--------|
| 1. JK = MN | 1. Given |
| 2. JK + KL = JL | 2. Segment Addition Postulate (K is between J and L) |
| 3. MN + KL = JL | 3. Substitution (Replace JK with MN) |

✔ Completed Proof

---

## 📝 Final Answers Summary:

Postulate Fill-in:

- If 3 points are collinear, and B is between A and C, then AB + BC = AC

---

Examples:

1. EF = 3
2. x = 5
3. TR = 27
4. x = 2, segments: 2, 17, 6
5. Proof completed as above.

---

Let me know if you'd like this formatted as a printable answer sheet!