Math Problem Statement

Use the diagram on the right to name all lines that are parallel to EL.

Solution

Let's examine the image and solve the problem step by step.

Problem:

You are asked to find all lines that are parallel to ELEL, using the diagram provided.

Shape Description:

The diagram shows a 3D shape, a parallelogram, with points A,B,C,D,E,F,G,H,J,LA, B, C, D, E, F, G, H, J, L. It is a hexagonal prism, where each line represents an edge of the figure. We are tasked with identifying lines that are parallel to the line segment ELEL.

Step-by-Step Solution:

  1. Line ELEL: The line ELEL is part of the hexagon (on the left side of the prism). Since prisms have parallel faces, any other edge on the same face of the hexagon will be parallel to this line.

  2. Identifying Parallel Lines: For this specific type of shape (a prism), the edges on opposite corresponding faces are parallel.

    • Looking at the left face, ELEL belongs to the side of the hexagon EJLFEJLF.
    • On the opposite side of the prism (the right face), the edges of the hexagon HGFDHGFD will have sides parallel to those of the left hexagon.

    Therefore, the following lines will be parallel to ELEL:

    • JFJF (opposite and corresponding side on the same face as ELEL)
    • LHLH (opposite face of the prism)
    • ABAB (parallel line on the right face of the prism)

Answer:

The correct answer from the options provided is: JF, AB, and LH\text{JF, AB, and LH}

Would you like any further explanation, or do you have questions on how we identified the parallel lines?

Related Questions:

  1. What property of prisms allows us to identify parallel lines easily?
  2. How can you determine whether two lines in 3D are parallel?
  3. What are the other sets of parallel lines in this prism?
  4. How does the shape of the prism influence the parallel lines?
  5. Can you find a real-world object with a similar shape to this prism?

Tip:

In 3D geometry, parallel lines often lie on opposite faces of a prism, but their orientation and direction must always remain the same!

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Math Problem Analysis

Mathematical Concepts

Geometry
3D Shapes
Parallel Lines
Prisms

Formulas

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Theorems

Properties of Prisms
Parallel Line Identification in 3D Shapes

Suitable Grade Level

Grades 7-10