Not a Simple Closed Curve: figure is closed, but the line of the figure intersects itself several times.
Basic Definitions: Triangles
Simple Closed Curves
[b][color=#ff0000][size=150][size=200]A Simple, Closed Curve is a closed curve that does not [url=https://www.mathopenref.com/intersection.html]intersect[/url] itself. [/size][/size][/color][/b]
Non-example
Non-Example
Not a Simple Closed Curve: The line does not intersect itself, but the figure is not closed.
Non-Example
Not a Simple Closed Curve: The line intersects itself, and the figure is not closed.
Example
A Simple Closed Curve: The figure is closed and the line does not intersect itself.
[size=200][size=150][b][color=#ff0000]When a simple closed curve is made up entirely of [/color][color=#0000ff][url=https://www.mathsisfun.com/definitions/line-segment.html]line segments[/url][/color][color=#ff0000], the figure is called a polygon. [br]The line segments that make up a polygon become its sides. [br] The endpoints of the line segments are [/color][color=#0000ff][url=https://www.mathopenref.com/vertex.html]vertices[/url][/color][color=#ff0000] of the polygon. [br]The (interior) angles of a polygon are the angles formed by two adjacent sides. [br][/color][/b][/size][/size]
Non-Example
Not a Polygon. The figure is closed, but the closed curve is not made up entirely of line segments.
Non-Example
Not a Polygon. The figure is made up entirely of line segments, but the figure is not closed.
Example
Polygon: The figure is closed and made up entirely of line segments.
[size=200][b][color=#ff0000]The polygon with the fewest number of sides is a TRIANGLE, which has three sides. [/color][/b][/size]
Triangle
A triangle is a polygon with the fewest number of sides.
[size=200][b][color=#0000ff]A triangle has three angles and therefore has three vertices[/color][/b][/size]
Naming the vertices and sides of a triangle
A triangle is a polygon with the fewest number of sides.
[b][color=#0000ff][size=150]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. [/size][/color][/b]