I"m i m really sorry if this is an extremely straightforward question, yet I"m honestly having actually a tough time understanding a theorem in mine geometry book. Here is the theorem:

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

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

"If 2 lines intersect, climate they crossing in exactly one point."

and three noncollinear points define a plane.

You are watching: A plane containing two points of a line contains the entire line

Now, a heat endlessly proceeds in two opposite directions, if two lines were to intersect, do not do it that produce $5$ points? and I"m also wondering if the would create two various planes (with both planes sharing one suggest 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 can clear up some misunderstanding. A heat contains more than simply two points. A heat is made up of infinitely plenty of points. The is however true the a line is established by 2 points, specific just extend the line segment connecting those 2 points.

Similarly a aircraft is established by 3 non-co-linear points. In this situation the three points are a suggest from every line and the suggest of intersection. We room not developing a brand-new point once the lines intersect, the allude was currently there.

This is not the exact same thing as saying that there room 5 points due to the fact that there space two from each line and the suggest from their intersection.


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reply Feb 24 "16 in ~ 21:18
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Michael MenkeMichael Menke
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Two unique lines intersecting in ~ one allude are had in part plane: merely take the intersection suggest and one various other in every line; the 3 noncollinear points define a airplane and the plane contains the lines.

In order to watch that over there is no other airplane containing the 2 lines, notice that any type of such airplane necessarily consists of the three former points and also since three noncollinear points define a plane, it need to be the airplane in the former paragraph.


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answer Feb 24 "16 in ~ 21:18
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man BJohn B
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First, a line includes infinitely many points. The idea right here is the if you have actually two distinct lines i m sorry intersect, there is only one (unique) aircraft that has both present and all of their points.

Try visualizing a plane that consists of two intersecting lines:

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Notice the if you then shot to "twist" that plane in some means that it will certainly no much longer contain both lines. In other words, there is no other airplane that can contain both lines, over there is just one.


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answer Feb 24 "16 at 21:19
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CarserCarser
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Think the a chair"s 4 legs. To examine that the 4 legs have the very same length. Pull 2 strings connecting bag of the opposite legs, every string is attached at the bottom the the legs. If the strings touch each various other in the center then the chair is stable (the one plane), otherwise that is wobbly (no plane).


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answer Feb 24 "16 in ~ 21:27
Oskar LimkaOskar Limka
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