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Pentagon (2d)

A pentagon is a polygon, a closed two-dimensional shape with five straight sides and five angles. The word "pentagon" comes from the Greek words "penta" (five) and "gonia" (angle). Here are some key properties of pentagons:

Sides and Angles:

A pentagon always has 5 sides and 5 interior angles.

Sum of Interior Angles:

The sum of the interior angles of any simple pentagon is always 540°.

Regular vs. Irregular:

- A regular pentagon has five equal sides and five equal interior angles (each measuring 108°). It is also equiangular and equilateral.
- An irregular pentagon has sides of different lengths and angles of different measures.

Convex vs. Concave:

- A convex pentagon has all its interior angles less than 180°, and all its vertices point outwards.
- A concave pentagon has at least one interior angle greater than 180°, and at least one vertex points inwards.

Diagonals:

A pentagon has 5 diagonals, which are line segments connecting non-adjacent vertices.

Symmetry (Regular Pentagon):

A regular pentagon has 5 lines of reflectional symmetry and rotational symmetry of order 5 (through 72°, 144°, 216°, and 288°).