Polygons Study Guide
Explain how to use the number of sides to find the sum of the interior angles of polygons.
(n-2) x 180 = the sum of the interior angles of a polygon
Explain how to use the number of sides to find one angle measure of a regular polygon.
(n-2) x 180 = the sum of the interior angles of a polygon. Divide this number by the number of sides.
Sum of the interior angles of a polygon
(n-2) x 180 where n is the number of sides on the polygon
Find the measure of one interior angle for a regular pentagon.
108 degrees
What is the measure of one angle of a regular hexagon?
120 degrees
Find the sum of the interior angles of a nonagon.
1260 degrees
Find the measure of one interior angle for a regular octagon
135 degrees
What is the measure of one angle of a regular nonagon?
140 degrees
Find the sum of the interior angles of a decagon.
1440 degrees
Find the measure of one interior angle for a regular 12 sided figure.
150 degrees
Find the sum of the interior angles of a 18-gon.
2880 degrees
Find the sum of the interior angles of a hexagon.
720 degrees
Polygon
A closed plane figure created by three or more line segments that intersect only at their endpoints (vertices)
Regular Polygon
A polygon with congruent sides and angles
triangle
A three sided polygon.
scalene triangle
A triangle that has NO congruent sides; all side lengths are different.
acute triangle
A triangle with all angles measures less than 90 degrees.
isosceles triangle
A triangle with at least two congruent sides; two side lengths are the same.
right triangle
A triangle with one 90 degree angle.
obtuse
A triangle with one obtuse angle; one angle measure is greater than 90 degrees.
equilateral triangle
A triangle with three congruent sides; all side lengths have the same measure.
A rectangle is a regular polygon. True or False
False. A rectangle has congruent angles, but it does not have congruent sides.
Angles of a regular polygon are not equal. True or False
False. Regular polygons have angles with congruent measurements.
Congruent
Having the same size and shape
leg
In a right triangle, the legs are the two sides which create the right angle; the perpendicular line segments.
hypotenuse
In a right triangle, the side opposite the right angle; the longest side in a right triangle. The side of the triangle that is does not create the right angle.
What are the differences between a regular and an irregular polygon?
Regular polygons have side and interior angle measurements that are are congruent.Irregular polygons do not have congruent side or interior angle measurements.
What is the easiest way to triangulate a polygon?
Start from one vertex to draw non-intersecting diagonals.
The measure of each interior angle of a regular polygon
Sum of the interior angles / number of sides
Explain how to use the number of sides to determine the number of triangles needed to triangulate the figure.
The number of sides minus 2 is equal to the number of triangles.
Explain how triangulating a polygon can be used to find the sum of the interior angles of a polygon.
The number of triangles multiplied by the 180 is equal to the sum of the interior angles.
Triangulate or Triangulation
The process of dividing a polygon into triangles by drawing its diagonals
triangle inequality
The rule that says the smallest side length plus the medium side length must have a sum greater than the largest side length. Small + Medium > Large
triangle sum theorem
The theorem which states that the angles measures of any triangle must have a sum of 180 degrees; the angles of a triangle add up to 180 degrees.
A square is a regular polygon. True or False
True. A square has congruent angles and sides so it is a regular polygon.
A regular pentagon and an irregular pentagon both have the same total interior angle measurement. True or False
True. It does not matter if a polygon is regular or irregular. The interior angle measure is always the same.
Regular polygons have both congruent sides and congruent angles. True or False
True. Regular polygons have congruent angles and sides.
Why is it important to know if a polygon is regular or irregular when determining angle measurements?
With regular polygons you can use the rule (n-2)x180/n. With irregular polygons you cannot use this rule because the angles are not congruent.
10 sided shape
decagon
12 sided shape
dodecagon
11 sided shape
hendecagon or an 11-gon
6 sided shape
hexagon
Number of triangles formed when a polygon is divided into triangles using diagonals (triangulation)
n-2 (n is the number of sides)
9 sided shape
nonagon
8 sided shape
octagon
15 sided shape
pentadecagon
5 sided shape
pentagon
4 sided shape
quadrilateral
7 sided shape
septagon or heptagon
3 sided shape
triangle
