Math Problem Statement

Name two planes that intersect in WX in the figure to the right.

Solution

To solve the problem, we need to identify two planes that intersect along the line WXWX in the given diagram of a rectangular prism.

From the diagram, the line WXWX connects points WW and XX and is the intersection of two planes that share this line.

  • Plane 1: The plane formed by W,X,V,UW, X, V, U (denoted as plane VUXVUX) contains the line WXWX.
  • Plane 2: The plane formed by W,X,S,TW, X, S, T (denoted as plane XTSXTS) also contains the line WXWX.

Now, checking the answer options:

  • A. Plane VUX and Plane VWS: Incorrect, as VWS doesn't intersect in line WXWX.
  • B. Plane UVR and Plane XTS: Incorrect, UVR doesn't intersect at WXWX.
  • C. Plane UVW and Plane UVR: Incorrect, neither of these planes contains WXWX.
  • D. Plane UVW and Plane XTS: Correct! Both planes UVW and XTS intersect in WXWX.

Thus, the correct answer is D.

Let me know if you would like a detailed breakdown or have any questions!

Here are 5 related questions to explore:

  1. What is a plane in geometry, and how do you define it?
  2. How do you determine the intersection line between two planes?
  3. What are the properties of a rectangular prism in 3D geometry?
  4. How can you calculate the angle between two intersecting planes?
  5. How do you determine the equation of a plane given three points?

Tip: When determining the intersection of planes, always look for shared edges or lines within the geometry.

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Math Problem Analysis

Mathematical Concepts

Geometry
Planes and Intersections
3D Shapes

Formulas

-

Theorems

Planes Intersecting Along a Line

Suitable Grade Level

Grades 8-10