Video: Identifying the Relationship between Two Planes

Which of the following statements is true about the two planes? [A] The two planes are coincident. [B] The two planes are parallel. [C] The two planes are intersected.

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Video Transcript

Which of the following statements is true about the two planes? a) The two planes are coincident, b) the two planes are parallel, or c) the two planes are intersected.

To solve this problem, we’ll need to think about the definition of coincident, parallel, and intersected.

Coincident planes lie exactly on top of each other. Here is the first plane and here is the second plane. You can’t see both of them at the same time because they’re on top of each other. In our example, we’re able to see planes 𝑋 and 𝑌, which means they cannot possibly be coincident.

What about option b? The two planes are parallel. Parallel planes are equidistant from one another. At all points, they are the same distance from each other. And that means that they never cross, they never touch. They would look something like this: these two planes never intersect.

Planes 𝑋 and 𝑌 intersect at this blue line. They cannot be parallel. And option c is the option where they are intersecting, which is true. At the blue line, there is an intersection of planes 𝑋 and 𝑌.

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