Definition: The triangles of a polygon are the triangles created by drawing
line segments from one
vertex of a polygon to all the others.

Try this Adjust the number of sides of the polygon below, or drag a vertex
to note the number of triangles inside the polygon.

Why? The triangles are created by drawing the
diagonals from one
vertex to all the others.
Since there would be no diagonal drawn back to itself,
and the diagonals to each adjacent vertex would lie on top of the adjacent sides,
the number of diagonals from a single vertex is three less the the number of sides, or n-3.
The number of triangles is one more than that, so n-2.

This can be used as another way to calculate the sum of the interior angles of a polygon. The interior angles of a triangle always sum to 180°. The number of triangles is n-2 (above). Therefor the interior angles of the polygon must be the sum of all the triangles' interior angles, or 180(n-2).

For most concave , irregular polygons , the triangles are of little practical use.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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