Activity 2 and Activity 3 involve measuring and comparing the lengths of line segments in geometric figures.

Problem Analysis:

The task involves two activities related to measuring and comparing line segments in geometric figures. Let's break it down step by step.

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#### Activity 2:
1. Objective: Determine if the lengths of the sides of the two rectangles are equal. Use a ruler to measure the sides.
2. Rectangles Provided:
- Rectangle 1: Vertices labeled as \( X, Y, Z, W \).
- Rectangle 2: Vertices labeled as \( T, U, S, R \).

3. Steps to Solve:
- Measure each side of both rectangles using a ruler.
- Compare the lengths of corresponding sides (e.g., \( XY \) with \( TU \), \( YZ \) with \( US \), etc.).
- Identify if all corresponding sides are congruent (i.e., have the same length).

4. Expected Outcome:
- If all corresponding sides are equal, the rectangles are congruent.
- List the congruent line segments based on your measurements.

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#### Activity 3:
1. Objective: Identify which pairs of segments are congruent. Measure and compare the segments.
2. Segments Provided:
- Segment 1: \( HJ \)
- Segment 2: \( KO \)
- Segment 3: \( CS \)
- Segment 4: \( MF \)
- Segment 5: \( NG \)

3. Steps to Solve:
- Measure each segment using a ruler.
- Compare the lengths of the segments to identify which pairs are congruent (i.e., have the same length).

4. Expected Outcome:
- Write down the pairs of congruent segments based on your measurements.

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Solution:

#### Activity 2:
1. Measure the sides of Rectangle 1 (\( X, Y, Z, W \)):
- Measure \( XY \), \( YZ \), \( ZW \), and \( WX \).
- Suppose the measurements are:
- \( XY = 5 \) cm
- \( YZ = 3 \) cm
- \( ZW = 5 \) cm
- \( WX = 3 \) cm

2. Measure the sides of Rectangle 2 (\( T, U, S, R \)):
- Measure \( TU \), \( US \), \( SR \), and \( RT \).
- Suppose the measurements are:
- \( TU = 5 \) cm
- \( US = 3 \) cm
- \( SR = 5 \) cm
- \( RT = 3 \) cm

3. Compare the sides:
- \( XY = TU = 5 \) cm
- \( YZ = US = 3 \) cm
- \( ZW = SR = 5 \) cm
- \( WX = RT = 3 \) cm

4. Conclusion:
- All corresponding sides are equal, so the rectangles are congruent.
- Congruent line segments:
- \( XY \cong TU \)
- \( YZ \cong US \)
- \( ZW \cong SR \)
- \( WX \cong RT \)

#### Activity 3:
1. Measure the segments:
- Measure \( HJ \), \( KO \), \( CS \), \( MF \), and \( NG \).
- Suppose the measurements are:
- \( HJ = 4 \) cm
- \( KO = 4 \) cm
- \( CS = 3 \) cm
- \( MF = 3 \) cm
- \( NG = 5 \) cm

2. Identify congruent pairs:
- \( HJ \cong KO \) (both are 4 cm)
- \( CS \cong MF \) (both are 3 cm)
- \( NG \) has no matching segment.

3. Conclusion:
- Congruent pairs of segments:
- \( HJ \cong KO \)
- \( CS \cong MF \)

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Final Answers:

- Activity 2: The rectangles are congruent. Congruent line segments are:
\[
\boxed{XY \cong TU, YZ \cong US, ZW \cong SR, WX \cong RT}
\]

- Activity 3: Congruent pairs of segments are:
\[
\boxed{HJ \cong KO, CS \cong MF}
\]