Dissecting the triangle

Geometry Level 1

What is the maximum number of diagonals a triangles can have?

1 3 0 2

Akeel Howell by Akeel Howell , 22, USA

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2 solutions

Hana Wehbi
Jul 7, 2017

A diagonal is a segment that joins two non consecutive vertices in a polygon. Since in a triangle this condition is non available so the number of diagonals is 0 0

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Akeel Howell
Jul 6, 2017

Triangles have no diagonals.

If we were to assume they did, we could calculate the number of diagonals as we would for any other regular polygon with n n sides: ( n 2 ) − n = n ( n − 3 ) 2 \dbinom n2 - n = \dfrac{n(n-3)}{2} .

With n = 3 n=3 , it is clear that triangles have no diagonals.

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The formula basically says: "Take all segments connecting two vertices and subtract those which make up the sides of the polygon." Obviously, in case of triangle that leaves nothing.

Marta Reece - 3 years, 11 months ago

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