Math Problem Statement

In the triangular prism shown below, which planes are parallel?

Solution

In the triangular prism shown in the image, we are asked to determine which planes are parallel. In a triangular prism, the two triangular bases are parallel to each other.

By analyzing the labels:

  • The triangle formed by the points STU is the top base.
  • The triangle formed by the points PQR is the bottom base.

Since these are the two triangular faces of the prism, STU and PQR are parallel planes.

Thus, the correct answer is: STU and PQR.

Would you like more details or have any further questions?

Here are five related questions to expand your understanding:

  1. What is the definition of parallel planes in geometry?
  2. How can you identify parallel planes in other types of prisms?
  3. Are the side faces of a triangular prism always rectangular?
  4. How do parallel planes relate to the concept of 3D geometry?
  5. Can parallel planes ever intersect?

Tip: When identifying parallel planes in 3D objects, always look for faces that have the same shape and orientation.

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Math Problem Analysis

Mathematical Concepts

3D Geometry
Parallel Planes
Prisms

Formulas

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Theorems

Parallel Planes Theorem

Suitable Grade Level

Grades 7-9