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Interior Angles Hall
Study Guide for the Interior Angles of Polygons
| Question | Answer |
|---|---|
| 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. |
| 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. |
| 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. |
| Find the sum of the interior angles of a nonagon. | 1260 degrees |
| Find the sum of the interior angles of a hexagon. | 720 degrees |
| Find the sum of the interior angles of a decagon. | 1440 degrees |
| Find the sum of the interior angles of a 18-gon. | 2880 degrees |
| Find the measure of one interior angle for a regular pentagon. | 108 degrees |
| Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees |
| Find the measure of one interior angle for a regular octagon | 135 degrees |
| 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. |
| What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals. |
| What is the measure of one angle of a regular hexagon? | 120 degrees |
| What is the measure of one angle of a regular nonagon? | 140 degrees |
| 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. |
| Angles of a regular polygon are not equal. True or False | False. Regular polygons have angles with congruent measurements. |
| Regular polygons have both congruent sides and congruent angles. True or False | True. Regular polygons have congruent angles and sides. |
| A rectangle is a regular polygon. True or False | False. A rectangle has congruent angles, but it does not have congruent sides. |
| A square is a regular polygon. True or False | True. A square has congruent angles and sides so it is a regular polygon. |
| 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. |
| scalene triangle | A triangle that has NO congruent sides; all side lengths are different. |
| equilateral triangle | A triangle with three congruent sides; all side lengths have the same measure. |
| obtuse | A triangle with one obtuse angle; one angle measure is greater than 90 degrees. |
| triangle | A three sided polygon. |
| 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. |
| 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. |
| 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 |
| 3 sided shape | triangle |
| 4 sided shape | quadrilateral |
| 5 sided shape | pentagon |
| 6 sided shape | hexagon |
| 7 sided shape | septagon or heptagon |
| 8 sided shape | octagon |
| 9 sided shape | nonagon |
| 10 sided shape | decagon |
| 11 sided shape | hendecagon or an 11-gon |
| 12 sided shape | dodecagon |
| 15 sided shape | pentadecagon |
| Sum of the interior angles of a polygon | (n-2) x 180 where n is the number of sides on the polygon |
| Number of triangles formed when a polygon is divided into triangles using diagonals (triangulation) | n-2 (n is the number of sides) |
| The measure of each interior angle of a regular polygon | Sum of the interior angles / number of sides |
| Triangulate or Triangulation | The process of dividing a polygon into triangles by drawing its diagonals |
| 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 |
| Congruent | Having the same size and shape |
| 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. |
| 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. |
| 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. |
| Find the sum of the interior angles of a nonagon. | 1260 degrees |
| Find the sum of the interior angles of a hexagon. | 720 degrees |
| Find the sum of the interior angles of a decagon. | 1440 degrees |
| Find the sum of the interior angles of a 18-gon. | 2880 degrees |
| Find the measure of one interior angle for a regular pentagon. | 108 degrees |
| Find the measure of one interior angle for a regular 12 sided figure. | 150 degrees |
| Find the measure of one interior angle for a regular octagon. | 135 degrees |
| 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. |
| What is the easiest way to triangulate a polygon? | Start from one vertex to draw non-intersecting diagonals. |
Created by:
theboss1000
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