WEBVTT
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Find three planes that pass through both of the points π΅ and πΆ.
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A plane is a space that extends infinitely in all directions and is a set of all points in three dimensions.
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Hereβs an example of a plane.
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We will call this plane plane πΎπΏπ.
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We label a plane by three points that are found not on the same line.
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Letβs consider the shape we were given.
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We need a plane that passes through point π΅ and πΆ.
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Since we know that a plane needs to be named by three points, we can choose a third point like point π·.
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And we would say that there is a plane that includes point, π΅, πΆ, and π·.
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This plane would include the face that is the bottom of this rectangular prism.
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It would include the face π΄π΅πΆπ·.
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But our goal is to find three different planes.
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So we need to consider another third point that would form a plane with the points π΅ and πΆ.
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We could try π΅, πΆ, and πΆ prime.
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They lie on the same plane.
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We could label this plane as plane π΅πΆπΆ prime.
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Itβs the plane that includes the front face of this rectangular prism, the face π΅πΆπΆ prime π΅ prime.
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What about a third plane?
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Again, weβll need the points π΅ and πΆ.
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This one might not seem as immediately obvious.
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But π΅, πΆ, and π· prime also fall in a plane.
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You can kind of imagine that this plane runs as a diagonal through our rectangular prism.
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We will call this one π΅πΆπ· prime.
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And so we have a list of three planes that pass through the points π΅ and πΆ.
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Now letβs go back to the plane π΅πΆπ·.
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Thatβs the yellow plane that includes the base of the rectangular prism.
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Remember that we just need three points to name this plane.
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And so we could also call it π΅πΆπ΄ or π·π΄π΅.
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If we named it π·π΄π΅, it would still be a correct answer, as the plane π·π΄π΅ includes the points π΅ and πΆ.
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In fact, this is true for all of our planes.
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We could name them in many different ways.
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We could name the plane that includes the front face π΅π΅ prime πΆ prime.
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We could name the diagonal plane that cuts through our prism π΄ prime π· prime πΆ.
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So long as we include three points from that plane.