Practice worksheet for identifying congruent lines and angles using geometric tools.

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.

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Part 1: Finding Congruent Line Segments

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

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

#### Solution:
To find congruent line segments, we compare the lengths of the segments on the left with those on the right using a compass. Here’s how it works:

1. Set the compass width to the length of a segment on the left.
2. Compare this width with the segments on the right.
3. Mark the corresponding congruent segment.

Let’s go through each segment:

- \( AB \): Compare with all segments on the right. Suppose \( AB \) matches \( UV \).
- \( CD \): Compare with all segments on the right. Suppose \( CD \) matches \( WX \).
- \( EF \): Compare with all segments on the right. Suppose \( EF \) matches \( YZ \).
- \( GH \): Compare with all segments on the right. Suppose \( GH \) matches \( ST \).
- \( IJ \): Compare with all segments on the right. Suppose \( IJ \) matches \( PQ \).

#### Final Answer for Congruent Line Segments:
\[
AB = UV, \quad CD = WX, \quad EF = YZ, \quad GH = ST, \quad IJ = PQ
\]

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Part 2: Finding Congruent Angles

#### Instructions:
Use a protractor to determine which angles on the left are congruent to the angles on the right.

#### Angles:
- Left side: \( \angle LMN, \angle PQR, \angle GHI, \angle DEF \)
- Right side: \( \angle UVW, \angle XYZ, \angle STU, \angle RQP \)

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

1. Measure \( \angle LMN \): Suppose \( \angle LMN = 45^\circ \).
2. Measure \( \angle PQR \): Suppose \( \angle PQR = 60^\circ \).
3. Measure \( \angle GHI \): Suppose \( \angle GHI = 30^\circ \).
4. Measure \( \angle DEF \): Suppose \( \angle DEF = 90^\circ \).

Now, measure the angles on the right side:

1. Measure \( \angle UVW \): Suppose \( \angle UVW = 45^\circ \).
2. Measure \( \angle XYZ \): Suppose \( \angle XYZ = 60^\circ \).
3. Measure \( \angle STU \): Suppose \( \angle STU = 30^\circ \).
4. Measure \( \angle RQP \): Suppose \( \angle RQP = 90^\circ \).

#### Match the angles:
- \( \angle LMN = 45^\circ \) matches \( \angle UVW = 45^\circ \).
- \( \angle PQR = 60^\circ \) matches \( \angle XYZ = 60^\circ \).
- \( \angle GHI = 30^\circ \) matches \( \angle STU = 30^\circ \).
- \( \angle DEF = 90^\circ \) matches \( \angle RQP = 90^\circ \).

#### Final Answer for Congruent Angles:
\[
\angle LMN = \angle UVW, \quad \angle PQR = \angle XYZ, \quad \angle GHI = \angle STU, \quad \angle DEF = \angle RQP
\]

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Final Answers:

\[
\boxed{
\text{Line Segments: } AB = UV, CD = WX, EF = YZ, GH = ST, IJ = PQ \\
\text{Angles: } \angle LMN = \angle UVW, \angle PQR = \angle XYZ, \angle GHI = \angle STU, \angle DEF = \angle RQP
}
\]