POLYGONS

A closed plane figure formed by connecting three or more segments at their endpoints is called a polygon. The segments are the sides of the polygon while the endpoints of this segments are the vertices of the polygon. Two sides of a polygon are adjacent or consecutive if they have a common endpoints. Two angles of polygon are adjacent if they have a side in common. Two vertices of a polygon are adjacent if they are the endpoints of a side.

KINDS OF POLYGONS

A. TRIANGLE

A triangle is a polygon with three sides. Every triangle has three altitudes, medians and angle bisectors. 

An altitude to a side is the segment drawn from a vertex of a triangle to the point on the line containing the opposite side such that the segment and the line intersect to form right angles.

A median to a side is a congruent drawn from a vertex of a triangle to the midpoint of the opposite side.

CLASSIFICATION OF TRIANGLE

table 1.1

Triangles can be classified according to the number of congruent sides and their angles.

Equilateral, isosceles and scalene triangles may be classified according to their congruent sides.

Acute, Obtuse and right triangles may be classified according to their angles.

In addition, equiangular triangle may be classified according to its angles. 

B. QUADRILATERALS

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.

The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees of arc, that is

 

This is a special case of the n-gon interior angle sum formula (n − 2) × 180°. In a crossed quadrilateral, the interior angles on either side of the crossing add up to 720°. All convex quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.

KINDS OF QUADRILATERALS

C. OTHER POLYGONS

1. Pentagon                       5 sides             5 corners           5 edges
2. Hexagon                       6 sides             6 corners            6 edges
3. Heptagon                      7 sides             7 corners            7 edges 
4. Octagon                        8 sides             8 corners            8 edges
5. Nonagon                       9 sides             9 corners            9 edges 
6. Decagon                      10 sides           10 corners          10 edges
7. Undecagon                  11 sides            11 corners          11 edges
8. Dodecagon                  12 sides           12 corners          12 edges 
9. n-gon                            n sides              n corners            n edges