# Diagonals in Geometry

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A series of free, online High School Geometry Video Lessons.
Examples, solutions, videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

• how to determine the number of diagonals in a polygon
• how to use mathematical model to determine the number of handshakes possible in a group of certain number of people

The following diagram gives the formula for the number of diagonals in an n-sided polygon. Scroll down the page for more examples and solutions. ### Number of Diagonals in a Polygon

A diagonal is a segment that connects two non-consecutive vertices in a polygon. The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n - 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice).
How to determine the number of diagonals in a polygon?

### Number of Handshakes

Mathematical modeling is used to generate a formula for the number of handshakes possible. The situation essentially asks how many sides and diagonals are in a given polygon and generates the triangle numbers: 1, 3, 6, 10, 15,
How to determine the number of handshakes possible in a group of certain number of people.

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