Download Geometry 6-1 Properties of Polygons

Geometry 6-1 Properties of Polygons
• Polygon: multi-sided shaped.
– Traits: straight lines, lines don’t cross, closed
Polygons
Not Polygons
Parts of a Polygon
Diagonal: segment that connects two
nonconsecutive vertices
Names of Polygons
Definitions
• Convex: all diagonals are inside the shape.
• Concave: at least one diagonal goes outside
the shape.
• Regular polygon: a polygon that is convex,
equilateral, and equiangular
• A polygon that is not regular is irregular
Tell whether the follow polygons are
regular/irregular and concave/convex.
irregular, convex
regular, convex
irregular, concave
regular, convex
Geometry 6-1 Interior and Exterior
Angles of Polygons
• Draw the following shapes:
– Triangle
– Rectangle (Quadrilateral)
– Pentagon
– Hexagon
– Octagon
• Draw all possible diagonals from one of the
vertices.
Table
n (# of sides)
3
4
5
6
7
8
n
# of Triangles
Sum of Interior
Angles
Table
n (# of sides)
# of Triangles
Sum of Interior
Angles
3
4
5
6
7
1
2
3
4
5
180°
360°
540°
720°
900°
8
n
6
(n - 2)
1080°
(n – 2) x 180°
Example
• Find the sum of each interior angle of a
regular 25-gon.
(25 – 2) x 180 = 4140° for all 25 angles
4140° / 25 = 165.6° for each angle
Measure of Exterior Angles
The sum of the exterior angles of a convex
polygon is always 360°.
Example:
Find the measure of each exterior angle of a regular
hexagon.
360° / 6 = 60° for each exterior angle