Math Problem Statement

Classify the line segments EH and DH in the given 3D figure.

Solution

To classify the segments EHEH and DHDH in the given 3D shape, let's analyze their properties:

  1. Parallel Segments: Two segments are parallel if they lie in the same plane and never intersect.
  2. Perpendicular Segments: Two segments are perpendicular if they intersect at a 90-degree angle.
  3. Skew Segments: Two segments are skew if they do not lie in the same plane and do not intersect.
  4. Parallel Planes: This refers to planes, not segments, being parallel to each other.

Analysis:

  • Segment EHEH is on the bottom face of the shape, connecting EE to HH.
  • Segment DHDH connects points DD and HH but does not lie on the same plane as EHEH.
  • Since EHEH and DHDH are neither in the same plane nor do they intersect, they meet the criteria for being skew segments.

Conclusion:

The correct answer is:

  • Skew Segments

Would you like a deeper explanation on skew lines, or do you have any other questions?


Here are some related questions to explore:

  1. How can we identify parallel lines in three-dimensional figures?
  2. What are real-world examples of skew lines?
  3. How do skew lines differ from intersecting lines in terms of geometry?
  4. Why can't two skew lines ever intersect?
  5. How are perpendicular segments identified in 3D geometry?

Tip: In 3D geometry, lines that do not intersect and are not parallel are always skew!

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Math Problem Analysis

Mathematical Concepts

3D Geometry
Parallel and Perpendicular Lines
Skew Lines

Formulas

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Theorems

Properties of Skew Lines
Definition of Parallel and Perpendicular Lines in 3D

Suitable Grade Level

Grades 9-10