Ch 11 Polygons What is a polygon Polygons

What is a polygon? Polygons are many-sided figures, with sides that are line segments.

Isosceles Triangles Two sides of equal length Three acute angles Sum of angles =

Equilateral Triangles All sides equal length Three acute angles Sum of angles = 180°

Scalene Triangles No sides are equal No angles are equal May have obtuse angle

Rectangles (Quadrilateral) Opposite sides are parallel Opposite side are equal in length 4 sides

Squares (Quadrilateral) All sides equal All angles equal and are 90 ° each Sum

Trapezoids (Quadrilateral) Two sides are parallel Has obtuse and acute angles Sometimes has a

Rhombuses (rhombi) (Quadrilateral) All four sides of equal length Opposite angles are equal –

Parallelograms (Quadrilateral) Opposite sides parallel Opposite sides equal in length Opposite angles equal Sum

Pentagons 5 sides Sum of angles = 540 ° 360 ° + 180 °

Hexagons 6 sides Sum of angles = 720 ° 540 ° + 180 °

Heptagon 7 sides Sum of angles = 900 ° 720 ° + 180 °

Octagons 8 sides Sum of angles = 1080 ° 900 ° + 180 °

Nonagon 9 sides Sum of angles = 1260 ° 1080 ° + 180 °

Decagons 10 sides Sum of angles = 1440° 1260 ° + 180 ° Can

There seems to be an "official“ set of names for polygons, uniformly derived from

After about 6 sides mathematicians usually refer to these polygons as n-gons. So

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Ch 11 Polygons

What is a polygon? Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have. Can be “regular” – all sides and all angles are equal to each other

Isosceles Triangles Two sides of equal length Three acute angles Sum of angles = 180°

Equilateral Triangles All sides equal length Three acute angles Sum of angles = 180° Is a regular polygon

Scalene Triangles No sides are equal No angles are equal May have obtuse angle Sum of angles = 180 °

Rectangles (Quadrilateral) Opposite sides are parallel Opposite side are equal in length 4 sides Each angle equals 90° Sum of angles = 360°

Squares (Quadrilateral) All sides equal All angles equal and are 90 ° each Sum of angles = 360 ° Is a regular polygon

Trapezoids (Quadrilateral) Two sides are parallel Has obtuse and acute angles Sometimes has a right angle Sum of angles = 360 °

Rhombuses (rhombi) (Quadrilateral) All four sides of equal length Opposite angles are equal – 2 acute angles, 2 obtuse angles Sum of angles = 360 ° Regular polygon

Parallelograms (Quadrilateral) Opposite sides parallel Opposite sides equal in length Opposite angles equal Sum of angles = 360 °

Pentagons 5 sides Sum of angles = 540 ° 360 ° + 180 ° Regular polygon

Hexagons 6 sides Sum of angles = 720 ° 540 ° + 180 ° Can be regular polygon

Heptagon 7 sides Sum of angles = 900 ° 720 ° + 180 ° Can be regular polygon

Octagons 8 sides Sum of angles = 1080 ° 900 ° + 180 ° Can be regular polygon

Nonagon 9 sides Sum of angles = 1260 ° 1080 ° + 180 ° Can be regular polygon

Decagons 10 sides Sum of angles = 1440° 1260 ° + 180 ° Can be regular polygon

There seems to be an "official“ set of names for polygons, uniformly derived from the Greek (after 4 sides). # of sides Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 hendecagon After about 6 sides 12 13 14 16 17 18 19 20 dodecagon tridecagon tetradecagon 15 pendedecagon hexdecagon heptdecagon octdecagon enneadecagon icosagon

After about 6 sides mathematicians usually refer to these polygons as n-gons. So a 13 sided polygon would be called a 13 gon.