Triangles- Can you draw a line that intersects

reagan3nc · #1 $Old$ 09-01-2008, 03:14 PM

Is it possible to draw a line that intersects exactly one side of a triangle(without passing through the vertex) Why or why not?

Is it possible to draw a line that intersects exactly two sides of a triangle?
Exactly 3 sides? Please explain.

I do not think that you can draw a line that intersects exactly one side, but i think you can draw one that intersects exactly two sides. I don't think you can draw one that intersects 3 sides because it would not be a line in order to intersect all three.

I am not sure about what i wrote. Could you please explain.

Plato · #2 $Old$ 09-01-2008, 03:45 PM

Quote:

Originally Posted by reagan3nc $View Post$

Is it possible to draw a line that intersects exactly one side of a triangle(without passing through the vertex) Why or why not?
Is it possible to draw a line that intersects exactly two sides of a triangle?
Exactly 3 sides? Please explain.

I do not think that you can draw a line that intersects exactly one side, but i think you can draw one that intersects exactly two sides. I don't think you can draw one that intersects 3 sides because it would not be a line in order to intersect all three.

Your answers on the first two are correct.
For the third question if the line includes a vertex and a point on the opposite side then the line intersects all three sides. However, if we exclude the any case in which the line may contain a vertex then the answer to the third question is no.
The explanation for these can be deep in the axiomatics concerning the separation of a plane by a line.