Problem Analysis:
The given image shows a 3D rectangular prism (or cuboid). The task is to identify pairs of congruent line segments in the shape. Congruent line segments are those that have the same length.
Step-by-Step Solution:
#### 1.
Understanding the Shape:
- The shape is a rectangular prism with vertices labeled as \( A, B, C, D, E, F, G, H \).
- Opposite edges of a rectangular prism are parallel and equal in length.
#### 2.
Identifying Congruent Line Segments:
- In a rectangular prism, the following pairs of edges are congruent:
- All edges parallel to each other are congruent.
- Specifically:
- Edges along the length (e.g., \( AB \) and \( DC \))
- Edges along the width (e.g., \( AD \) and \( BC \))
- Edges along the height (e.g., \( AE \) and \( BH \))
#### 3.
Analyzing the Given Pairs:
-
(1) \( \text{seg } AB \cong \text{seg } DC \):
- \( AB \) and \( DC \) are opposite edges of the top face of the prism.
- Since opposite edges in a rectangular prism are congruent, this statement is correct.
-
(2) \( \text{seg } AE \cong \text{seg } BH \):
- \( AE \) and \( BH \) are vertical edges connecting the top face to the bottom face.
- Since all vertical edges in a rectangular prism are congruent, this statement is correct.
-
(3) \( \text{seg } EF \cong \text{seg } \ldots \):
- \( EF \) is an edge on the bottom face of the prism.
- The edge congruent to \( EF \) is \( HG \), as they are opposite edges on the bottom face.
- Therefore, \( \text{seg } EF \cong \text{seg } HG \).
-
(4) \( \text{seg } DF \cong \text{seg } \ldots \):
- \( DF \) is a diagonal edge on the right face of the prism.
- The edge congruent to \( DF \) is \( CG \), as they are diagonals of congruent rectangles on opposite faces.
- Therefore, \( \text{seg } DF \cong \text{seg } CG \).
#### 4.
Final Answers:
- For (3): \( \text{seg } EF \cong \text{seg } HG \)
- For (4): \( \text{seg } DF \cong \text{seg } CG \)
Final Answer:
\[
\boxed{(3) \text{seg } EF \cong \text{seg } HG, \quad (4) \text{seg } DF \cong \text{seg } CG}
\]
Parent Tip: Review the logic above to help your child master the concept of congruent line segment worksheet.
