Math Problem Statement
Find each intersection. If no intersection, write none. Based on a diagram, specify if the intersection is a point, segment, or plane.
Solution
Let's analyze the image and solve each of the intersection questions based on the given geometric figure:
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Plane GLM and Plane LPN:
- These two planes share the line segment LM. Hence, their intersection is Segment LM.
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Segment GK and Segment LG:
- GK and LG meet at Point G because they share that common endpoint. Thus, the intersection is Point G.
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Plane HJN and Plane GKL:
- These two planes do not appear to share any line or segment based on the provided diagram, so the intersection is None.
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Segment KP and Plane KJN:
- KP lies on Plane KJN, and specifically, K is a shared point. Therefore, the intersection is Point K.
Summary of intersections:
- Plane GLM and Plane LPN: Segment LM
- Segment GK and Segment LG: Point G
- Plane HJN and Plane GKL: None
- Segment KP and Plane KJN: Point K
Let me know if you'd like further clarifications on any part of this!
Here are five related questions:
- What defines the intersection of two planes geometrically?
- How can we determine whether two segments intersect in 3D space?
- Can two non-parallel planes have no intersection at all?
- What conditions are necessary for a segment to lie entirely within a plane?
- Can three planes intersect at a single point? Why or why not?
Tip: When identifying intersections in geometric figures, always look for shared points, lines, or segments between the shapes!
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Math Problem Analysis
Mathematical Concepts
Geometry
Planes
Lines
Points
3D Space
Formulas
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Theorems
Intersection of Planes
Line and Plane Intersection
Suitable Grade Level
Grades 9-12