I"m i m really sorry if this is an extremely simple question, but I"m honestly having a difficult time understanding a to organize in mine geometry book. Below is the theorem:

"If 2 lines intersect, then precisely one airplane contains the lines."

Now, each line has two points, and according to another theorem in mine book:

"If two lines intersect, then they intersect in specifically one point."

and 3 noncollinear points specify a plane.

You are watching: If two planes intersect then their intersection is a line

Now, a line endlessly continues in 2 opposite directions, if 2 lines to be to intersect, do not do it that create $5$ points? and I"m likewise wondering if the would develop two various planes (with both planes share one suggest at the intersection.)


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edited Feb 24 "16 at 21:13
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Brian M. Scott
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I think I can clear up some misunderstanding. A heat contains much more than simply two points. A line is made up of infinitely countless points. It is but true that a heat is identified by 2 points, specific just extend the heat segment connecting those two points.

Similarly a aircraft is determined by 3 non-co-linear points. In this case the 3 points space a allude from every line and also the point of intersection. We space not producing a brand-new point as soon as the lines intersect, the allude was currently there.

This is no the exact same thing as saying that there room 5 points since there are two from every line and also the allude from their intersection.


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answered Feb 24 "16 at 21:18
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Michael MenkeMichael Menke
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Two unique lines intersecting in ~ one allude are included in some plane: just take the intersection point and one various other in each line; the 3 noncollinear points define a aircraft and the plane contains the lines.

In bespeak to see that there is no other aircraft containing the two lines, notification that any type of such airplane necessarily includes the three former points and also since three noncollinear points define a plane, it need to be the aircraft in the former paragraph.


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answered Feb 24 "16 at 21:18
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john BJohn B
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First, a line has infinitely numerous points. The idea right here is that if you have two distinctive lines i beg your pardon intersect, there is just one (unique) aircraft that contains both currently and every one of their points.

Try visualizing a aircraft that consists of two intersecting lines:

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Notice that if girlfriend then shot to "twist" that aircraft in some method that it will no longer contain both lines. In other words, over there is no other airplane that might contain both lines, over there is only one.


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CarserCarser
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Think the a chair"s 4 legs. To check that the 4 legs have the exact same length. Pull 2 strings connecting bag of the contrary legs, every string is attached at the bottom of the legs. If the strings touch each other in the middle then the chair is steady (the one plane), otherwise it is wobbly (no plane).


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answered Feb 24 "16 at 21:27
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