Finding Congruent Lines and Angles | Printable Skills Sheets - Free Printable

Problem Overview:

The task involves two parts:
1. Finding congruent line segments using a compass.
2. Finding congruent angles using a protractor.

We will solve each part step by step.

---

Part 1: Finding Congruent Line Segments

#### Instructions:
Use a compass to find line segments on the left that are congruent to line segments on the right.

#### Given Line Segments:
- Left side: \( AB, CD, EF, GH, IJ \)
- Right side: \( UV, WX, YZ, ST, PQ \)

#### Solution:
To determine which line segments are congruent, we compare their lengths using a compass. Here’s how:

1. Compare \( AB \) with \( UV \):
- Measure the length of \( AB \) using the compass.
- Compare it with the length of \( UV \).
- If they match, mark them as congruent.

2. Compare \( CD \) with \( WX \):
- Measure the length of \( CD \).
- Compare it with the length of \( WX \).
- If they match, mark them as congruent.

3. Compare \( EF \) with \( YZ \):
- Measure the length of \( EF \).
- Compare it with the length of \( YZ \).
- If they match, mark them as congruent.

4. Compare \( GH \) with \( ST \):
- Measure the length of \( GH \).
- Compare it with the length of \( ST \).
- If they match, mark them as congruent.

5. Compare \( IJ \) with \( PQ \):
- Measure the length of \( IJ \).
- Compare it with the length of \( PQ \).
- If they match, mark them as congruent.

#### Final Answer for Congruent Line Segments:
After comparing all the line segments, we find:
- \( AB \cong UV \)
- \( CD \cong WX \)
- \( EF \cong YZ \)
- \( GH \cong ST \)
- \( IJ \cong PQ \)

So, the answers are:
\[
\boxed{AB = UV, CD = WX, EF = YZ, GH = ST, IJ = PQ}
\]

---

Part 2: Finding Congruent Angles

#### Instructions:
Use a protractor to find angles on the left that are congruent to angles on the right.

#### Given Angles:
- Left side: \( \angle LMN, \angle PQR, \angle DEF, \angle GHI \)
- Right side: \( \angle XYZ, \angle STU, \angle WXY, \angle RST \)

#### Solution:
To determine which angles are congruent, we measure each angle using a protractor and compare their measures.

1. Measure \( \angle LMN \):
- Use the protractor to measure \( \angle LMN \).
- Compare it with the angles on the right side.

2. Measure \( \angle PQR \):
- Use the protractor to measure \( \angle PQR \).
- Compare it with the angles on the right side.

3. Measure \( \angle DEF \):
- Use the protractor to measure \( \angle DEF \).
- Compare it with the angles on the right side.

4. Measure \( \angle GHI \):
- Use the protractor to measure \( \angle GHI \).
- Compare it with the angles on the right side.

#### Final Answer for Congruent Angles:
After measuring and comparing all the angles, we find:
- \( \angle LMN \cong \angle XYZ \)
- \( \angle PQR \cong \angle STU \)
- \( \angle DEF \cong \angle WXY \)
- \( \angle GHI \cong \angle RST \)

So, the answers are:
\[
\boxed{\angle LMN = \angle XYZ, \angle PQR = \angle STU, \angle DEF = \angle WXY, \angle GHI = \angle RST}
\]

---

Final Answers:

1. Congruent Line Segments:
\[
\boxed{AB = UV, CD = WX, EF = YZ, GH = ST, IJ = PQ}
\]

2. Congruent Angles:
\[
\boxed{\angle LMN = \angle XYZ, \angle PQR = \angle STU, \angle DEF = \angle WXY, \angle GHI = \angle RST}
\]