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Math Help - Triangles- Can you draw a line that intersects

  1. #1
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    Triangles- Can you draw a line that intersects

    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.
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  2. #2
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    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.
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