Geometry practice worksheet focusing on measuring segments using number lines and algebraic expressions.

Let's solve each problem step by step from the worksheet titled "Geometry 1-2 Practice: Measuring Segments."

---

1. Find the length of each segment using the number line:

Points on the number line:
- P = -5
- Q = -2
- R = 4
- S = 5
- T = 8

#### 1. $\overline{PR}$
$$
PR = |R - P| = |4 - (-5)| = |4 + 5| = 9
$$
✔ Answer: 9

#### 2. $\overline{QT}$
$$
QT = |T - Q| = |8 - (-2)| = |8 + 2| = 10
$$
✔ Answer: 10

#### 3. $\overline{QS}$
$$
QS = |S - Q| = |5 - (-2)| = |5 + 2| = 7
$$
✔ Answer: 7

---

4–6. Use the number line with points G, H, I (in order)

We assume G–H–I are in that order on a line.

#### 4. If $GH = 31$ and $HI = 11$, then $GI =$
Since $GI = GH + HI$,
$$
GI = 31 + 11 = 42
$$
✔ Answer: 42

#### 5. If $GH = 45$ and $GI = 61$, then $HI =$
$$
HI = GI - GH = 61 - 45 = 16
$$
✔ Answer: 16

#### 6. If $GH = 7y + 3$, $HI = 3y - 5$, and $GI = 9y + 7$

We know:
$$
GI = GH + HI
$$
Substitute:
$$
9y + 7 = (7y + 3) + (3y - 5)
$$
Simplify right side:
$$
9y + 7 = 10y - 2
$$
Solve for $y$:
$$
9y + 7 = 10y - 2 \\
7 + 2 = 10y - 9y \\
9 = y
$$
✔ a. $y = 9$

Now find lengths:

- $GH = 7(9) + 3 = 63 + 3 = 66$
- $HI = 3(9) - 5 = 27 - 5 = 22$
- $GI = 9(9) + 7 = 81 + 7 = 88$

Check: $GH + HI = 66 + 22 = 88 = GI$ ✔

✔ b. $GH = 66$, $HI = 22$, $GI = 88$

---

7–9. Use the number line below:

Points:
- B = -15
- C = -10
- D = -5
- E = 0
- F = 2
- G = 6

#### 7. $\overline{CE}$ and $\overline{FD}$

- $CE = |E - C| = |0 - (-10)| = 10$
- $FD = |D - F| = |-5 - 2| = |-7| = 7$

So, $CE = 10$, $FD = 7$

Are they congruent? No (10 ≠ 7)

✔ Answer: CE = 10, FD = 7; not congruent

#### 8. $\overline{CD}$ and $\overline{FG}$

- $CD = |D - C| = |-5 - (-10)| = |-5 + 10| = 5$
- $FG = |G - F| = |6 - 2| = 4$

So, $CD = 5$, $FG = 4$

Not congruent.

✔ Answer: CD = 5, FG = 4; not congruent

#### 9. $\overline{GE}$ and $\overline{BD}$

- $GE = |E - G| = |0 - 6| = 6$
- $BD = |D - B| = |-5 - (-15)| = |-5 + 15| = 10$

So, $GE = 6$, $BD = 10$

Not congruent.

✔ Answer: GE = 6, BD = 10; not congruent

---

10–11. Use figure: K — L — M (in order)

#### 10. $KL = 3x + 2$, $LM = 5x - 10$

Assume K–L–M is a straight line, so $KM = KL + LM$. But we don't have KM. However, since no other info is given, we must assume this is just asking to find $KL$ if there’s an implied condition.

Wait — actually, there is no additional condition given like "KLM is a segment" or "L is midpoint", so unless more is known, we cannot solve unless we assume they are connected, but still need more.

But looking at structure: likely we are missing a diagram, but based on standard problems, perhaps it's implied that L is between K and M, and maybe KM is given? But it isn’t.

Wait — perhaps the intention is that KL and LM are parts of a line, and maybe KL = LM? But that's not stated.

Alternatively, maybe the total length isn't needed — but without another equation, we can't solve.

Wait — actually, perhaps this is a typo or missing info.

But let's check: maybe the question assumes that K, L, M are colinear with L between K and M, and we are to find $x$ such that the segments make sense?

But still, unless there's a relation (like KM = something), we can't solve.

Wait — look at #11: same pattern. So likely, these are meant to be solved using the fact that KL and LM are adjacent segments, but without additional info, we can't solve unless...

Wait — perhaps the only way to solve is if KL = LM? But again, not stated.

Alternatively, perhaps the problem assumes that L is the midpoint? But that's not said.

Wait — perhaps the original image had a diagram showing that KLM is a straight line, and KL and LM are expressed in terms of x, and KM is known? But it's not.

Hmm.

Wait — maybe the intention is that the segments are defined, and we are to find x such that the expressions are valid, but without constraints, infinite solutions.

Wait — perhaps there’s a typo. Let’s look at #11.

Maybe the problem is: KL and LM are segments, and you’re to find KL — but unless we know something about their relationship, we can’t.

But wait — perhaps the problem is incomplete? Or perhaps it's implied that K-L-M is a line, and we're to express KL, but without more data...

Wait — actually, this is a common type: often in such problems, KL and LM are parts of a whole, but here, no total is given.

Unless... perhaps in the diagram, point M is labeled at a coordinate? But not shown.

Wait — perhaps we should assume KL and LM are adjacent, and maybe KL = LM? But again, not stated.

Wait — maybe the problem is asking to find x such that KL and LM are equal? But that’s not what it says.

Let me re-read:

> For Exercises 10–11, use the figure below. Find the value of KL.

But no figure — only K—L—M.

Perhaps the intention is that KL and LM are adjacent segments, and there is a total length? But none is given.

Wait — unless in the original image, there was a number line with coordinates?

But since it's not visible, perhaps we assume standard problems where KL and LM are parts of a line, and KL + LM = KM, but KM not given.

Wait — unless the problem is: KL = 3x + 2, LM = 5x – 10, and L is the midpoint of KM? Then KL = LM.

That would make sense!

Let’s assume that L is the midpoint of KM, so $KL = LM$

Then:
$$
3x + 2 = 5x - 10 \\
2 + 10 = 5x - 3x \\
12 = 2x \\
x = 6
$$

Then $KL = 3(6) + 2 = 18 + 2 = 20$

✔ Answer: KL = 20

Similarly for #11.

Let’s try that assumption.

#### 10. Assume KL = LM (since L is midpoint)

As above:
$$
3x + 2 = 5x - 10 \Rightarrow x = 6 \Rightarrow KL = 20
$$
✔ Answer: 20

#### 11. $KL = 8x - 5$, $LM = 6x + 3$

Again, assume L is midpoint, so $KL = LM$

$$
8x - 5 = 6x + 3 \\
8x - 6x = 3 + 5 \\
2x = 8 \\
x = 4
$$

Then $KL = 8(4) - 5 = 32 - 5 = 27$

✔ Answer: 27

This is a common setup, so we'll go with that.

---

12. $\overline{XY}$ has endpoints at –13 and 23. What is the coordinate of its midpoint?

Use midpoint formula:
$$
\text{Midpoint} = \frac{-13 + 23}{2} = \frac{10}{2} = 5
$$

✔ Answer: 5

---

✔ Final Answers Summary:

1. $ \overline{PR} = 9 $
2. $ \overline{QT} = 10 $
3. $ \overline{QS} = 7 $
4. $ GI = 42 $
5. $ HI = 16 $
6. a. $ y = 9 $
b. $ GH = 66 $, $ HI = 22 $, $ GI = 88 $
7. $ \overline{CE} = 10 $, $ \overline{FD} = 7 $; not congruent
8. $ \overline{CD} = 5 $, $ \overline{FG} = 4 $; not congruent
9. $ \overline{GE} = 6 $, $ \overline{BD} = 10 $; not congruent
10. $ KL = 20 $
11. $ KL = 27 $
12. Midpoint = 5

---

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