   Chapter 2.5, Problem 39E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
9 views

# Consider a polygon of n sides deter-mined by the n noncollinear vertices A, B, C, D. and so on. a) Choose any vertex of the polygon. To how many of the remaining vertices of the polygon can the selected vertex be joined to form a diagonal?b) Considering that each of the n vertices in (a) can be joined to any one of the remaining ( n − 3 ) vertices to form diagonals, the product n ( n − 3 ) appears to represent the total number of diagonals possible. However, this number includes duplications, such as A C ¯ and C A ¯ . What expression actually represents D, the total number of diagonals in a polygon of n sides? .

To determine

a)

To find:

The number of the remaining vertices of the polygon can the selected vertex is joined to form a diagonal.

Explanation

Given:

The following figure shows the given diagram.

Calculation:

All vertex and can be joined to form a diagonal of polygon, except for the selected vertex and two neighborhood vertices of the selected vertex...

To determine

b)

To find:

The expression to represents D, the total number of diagonals in polygon of n sides.

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