Segment and Angle Addition Postulate Notes and Worksheets ... - Free Printable

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

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🔹 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.

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## ✔ Examples:

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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

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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

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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 means from T to R, which is TS + SR?

But actually, TR is the distance from T to R. Since R–S–T, we go backwards:
- TR = TS + SR = (3x - 4) + 7

Plug in x = 8:
- 3(8) - 4 = 24 - 4 = 20
- Add 7 → 20 + 7 = 27

So TR = 27

✔ Answer: TR = 27

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

Given:
- The whole segment = 10x + 5
- It's divided into three parts: x, x + 15, and 3x

So:
$$
x + (x + 15) + 3x = 10x + 5
$$
$$
x + x + 15 + 3x = 10x + 5
$$
$$
5x + 15 = 10x + 5
$$

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 should be: 10x + 5 = 10(2) + 5 = 25 ✔

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

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5. Complete the proof

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

Diagram shows:
- J — K — L (so K is between J and L)
- M — N (a separate segment)

But since JK = MN, and we want to prove MN + KL = JL, we’re using substitution.

| 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 Property of Equality (Replace JK with MN) |

✔ Completed Proof Table:

| Statements | Reasons |
|-----------|--------|
| 1. JK = MN | 1. Given |
| 2. JK + KL = JL | 2. Segment Addition Postulate |
| 3. MN + KL = JL | 3. Substitution (from statement 1) |

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## ✔ Final Answers Summary:

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

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