I"m i m really sorry if this is an extremely straightforward question, but I"m honestly having a hard time expertise a theorem in my geometry book. Right here is the theorem:

"If two lines intersect, then specifically one plane contains the lines."

Now, each line contains two points, and according to one more theorem in mine book:

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

and 3 noncollinear points specify a plane.

You are watching: The intersection of two distinct planes is a

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


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edited Feb 24 "16 in ~ 21:13
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Brian M. Scott
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I think I have the right to clear up some misunderstanding. A heat contains more than simply two points. A heat is consisted of of infinitely plenty of points. It is but true the a heat is established by 2 points, namely just prolong the line segment connecting those two points.

Similarly a airplane is determined by 3 non-co-linear points. In this case the 3 points are a allude from each line and the suggest of intersection. We space not developing a brand-new point when the present intersect, the suggest was currently there.

This is no the same thing together saying the there room 5 points due to the fact that there space two from each line and also the suggest from your intersection.


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answer Feb 24 "16 in ~ 21:18
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Michael MenkeMichael Menke
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Two distinct lines intersecting at one suggest are consisted of in some plane: simply take the intersection allude and one various other in each line; the three noncollinear points define a aircraft and the airplane contains the lines.

In order to see that there is no other airplane containing the two lines, an alert that any such airplane necessarily contains the three former points and since 3 noncollinear points specify a plane, it have to be the plane in the previous paragraph.


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man BJohn B
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First, a line includes infinitely plenty of points. The idea here is that if you have actually two distinct lines i m sorry intersect, there is only one (unique) aircraft that has both currently and all of their points.

Try visualizing a aircraft that consists of two intersecting lines:

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Notice the if friend then shot to "twist" that aircraft in some means that it will no much longer contain both lines. In other words, over there is no other aircraft that can contain both lines, over there is only one.


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answered Feb 24 "16 in ~ 21:19
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CarserCarser
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Think the a chair"s 4 legs. To check that the 4 legs have actually the very same length. Pull two strings connecting pairs of the contrary legs, every string is attached at the bottom the the legs. If the strings touch each other in the center then the chair is steady (the one plane), otherwise it is wobbly (no plane).


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answer Feb 24 "16 at 21:27
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