In a convex polygon with 2021 sides (called a 2021-gon), all diagonals are drawn. In other words, each vertex is joined by a line segment to every vertex to which it is not already connected by a side. A line intersects the 2021-gon but does not pass through any vertices. Prove that the line intersects an even number of diagonals.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In a convex polygon with 2021 sides (called a 2021-gon), all diagonals are drawn. In other words,
each vertex is joined by a line segment to every vertex to which it is not already connected by
a side. A line intersects the 2021-gon but does not pass through any vertices. Prove that the
line intersects an even number of diagonals.
Transcribed Image Text:In a convex polygon with 2021 sides (called a 2021-gon), all diagonals are drawn. In other words, each vertex is joined by a line segment to every vertex to which it is not already connected by a side. A line intersects the 2021-gon but does not pass through any vertices. Prove that the line intersects an even number of diagonals.
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