Geometry worksheet on the Segment Addition Postulate with examples, problems, and a proof.

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

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🔹 Segment Addition Postulate (Fill in the blanks):

> Segment Addition Postulate: If 3 points are collinear (on the same line segment), and B is between A and C, then
> AB + BC = AC

✔ So the completed sentence is:

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

From the diagram: D — E — F (E is between D and F)

So by 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 = 32

Since M — N — O (N is between M and O):

> 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 = 59

Points: R — S — T — U

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

Now find TR.
TR = ST + TU
ST = 3x - 4 = 3(8) - 4 = 24 - 4 = 20
TU = 4x = 4(8) = 32
So TR = 20 + 32 = 52

✔ Answer: TR = 52

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

Given:
- Total length = 10x + 5
- Segments: x, x + 15, 3x

These three segments add up to the total:
> x + (x + 15) + 3x = 10x + 5
> x + x + 15 + 3x = 10x + 5
> 5x + 15 = 10x + 5
> 15 - 5 = 10x - 5x
> 10 = 5x
> 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 → ✔ Correct

✔ Answer:
- x = 2
- Lengths: 2, 17, 6

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5. Complete the proof.

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

Diagram: J — K — L
and a separate segment M — N (but we’re told JK = MN)

We need to prove: MN + KL = JL

But we know from the diagram that J — K — L, so by Segment Addition Postulate:

> JK + KL = JL

We're given: JK = MN

So substitute:

> MN + KL = JL

Now fill in the table:

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

✔ Completed Proof:

| Statements | Reasons |
|-----------|--------|
| 1. JK = MN | 1. Given |
| 2. JK + KL = JL | 2. Segment Addition Postulate |
| 3. MN + KL = JL | 3. Substitution Property of Equality |

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✔ Final Answers Summary:

1. EF = 3
2. x = 5
3. TR = 52
4. x = 2, segments: 2, 17, 6
5. Proof completed with correct statements and reasons.

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