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Basic Definitions: Triangles

Simple Closed Curves

A Simple, Closed Curve is a closed curve that does not intersect itself.

Non-example

Non-example
Not a Simple Closed Curve: figure is closed, but the line of the figure intersects itself several times.

Non-Example

Non-Example
Not a Simple Closed Curve: The line does not intersect itself, but the figure is not closed.

Non-Example

Non-Example
Not a Simple Closed Curve: The line intersects itself, and the figure is not closed.

Example

Example
A Simple Closed Curve: The figure is closed and the line does not intersect itself.
When a simple closed curve is made up entirely of line segments, the figure is called a polygon. The line segments that make up a polygon become its sides. The endpoints of the line segments are vertices of the polygon. The (interior) angles of a polygon are the angles formed by two adjacent sides.

Non-Example

Non-Example
Not a Polygon. The figure is closed, but the closed curve is not made up entirely of line segments.

Non-Example

Non-Example
Not a Polygon. The figure is made up entirely of line segments, but the figure is not closed.

Example

Example
Polygon: The figure is closed and made up entirely of line segments.
The polygon with the fewest number of sides is a TRIANGLE, which has three sides.

Triangle

Triangle
A triangle is a polygon with the fewest number of sides.
A triangle has three angles and therefore has three vertices

Naming the vertices and sides of a triangle

Naming the vertices and sides of a triangle
A triangle is a polygon with the fewest number of sides.
When we label the vertices of a triangle with capital letters (ABC), the same lower case letters (abc) refer to the sides opposite the angle.