consider n>3 lines in general position in the plane. prove that these lines form at least n - 2 triangles. g

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30-11-2022
Mathematics

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consider n>3 lines in general position in the plane. prove that these lines form at least n - 2 triangles. g

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-03T18:14:04+01:00

In general, there are n>3 lines in the plane. Show that at least n - 2 triangles are formed by these lines.

Let's consider the following diagram, where each line is labelled with a letter:

A-B-C-D-E

Since each line intersects with at least one other line, there are at least n-2 triangles that can be formed. For example, triangle ABC, triangle ABD, triangle ABE, triangle BCD, triangle BDE, and triangle CDE are all triangles that can be formed from our five lines.

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