If two distinct planes intersect, then their intersection is a line. Which of the figures best describes the statement above?
The Correct Answer and Explanation is:
The correct answer is option d, which shows two distinct planes intersecting along a line.
In geometry, a plane is a flat surface that extends indefinitely in all directions. It is two-dimensional, meaning it has length and width but no thickness. When two planes are distinct and they intersect, they do so in exactly one line. This is a fundamental property of Euclidean space.
The reasoning behind this lies in how planes are defined. A single plane is determined by at least three non-collinear points. When a second plane intersects it, the only way for both sets of points and directions to meet, without fully overlapping, is along a shared set of points that form a line. That line represents every point that satisfies the equations of both planes at once.
Let’s examine why the other options are incorrect:
- Option a, a triangle, does not convey any spatial relationship between planes.
- Option b, a parallelogram with arrows, represents a flat surface but tells us nothing about an intersection between two planes.
- Option c, two intersecting lines, represents the intersection of two lines—not planes. Though lines may meet at a point, this does not help illustrate the intersection of surfaces.
Only option d provides a visual of two flat surfaces crossing each other and sharing a single straight edge. This edge is their line of intersection.
This principle is not just theoretical. It appears in real-world structures. For example, where two walls meet at a corner in a building, the edge where they join is a physical representation of this geometric concept.
Thus, option d is the best visual description of two intersecting planes with their common line.
