## Polygons

**Description:**

**Last Updated:**

**Subject(s):**- Mathematics
- Mathematics > Geometry

**Educational Level(s):**- Grades 9-10 / Ages 14-16
- Grades 11-12 / Ages 16-18

**Instructional Component Type(s):**- Curriculum: Unit

- Contributed By: Winpossible

### Getting Started - Polygons

**Description:**

This mini-lesson is an introduction to the basics of a polygon and will help learning about polygons. Polygon is a closed plane figure made up of several line segments that are joined together. The polygons are many-sided figures, and these are named according to the number of sides and angles they have. The most commonly known polygons are the triangle, the rectangle, and the square. You'll learn here with the help of video, and some examples with solution about the important properties of polygons and their relationship. Polygons also have diagonals, which are segments that join two vertices but no sides. It explains further about vertex of a polygon, sides of a polygon and the angles formed by it. E.g. A vertex is an endpoint of a line segment that forms a polygon. The line segments which form a polygon are called its sides and the angles formed by the line segments are known as the interior angles of a polygon. Polygons are named according to the number of sides and angles they have. For example, Triangle: 3 sides and 3 angles, Quadrilateral: 4 sides and 4 angles, Pentagon: 5 sides and 5 angles etc. In hexagon

*ABCDEF*, the vertices are

*A*,

*B*,

*C*,

*D*,

*E*and

*F*, the sides are

*AB*,

*BC*,

*CD*,

*DE*,

*EF*,

*FA*, and the angles are

*A*,

*B*,

*C*,

*D*,

*E*and

*F*.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

**Last Updated:**

**Subject(s):**- Mathematics
- Mathematics > Geometry

**Educational Level(s):**- Grades 9-10 / Ages 14-16
- Grades 11-12 / Ages 16-18

**Instructional Component Type(s):**- Asset: Video/Presentation/Slides

This mini-lesson is an introduction to the basics of a polygon and will help learning about polygons. Polygon is a closed plane figure made up of several line segments that are joined together. The polygons are many-sided figures, and these are named according to the number of sides and angles they have. The most commonly known polygons are the triangle, the rectangle, and the square. You'll learn here with the help of video, and some examples with solution about the important properties of polygons and their relationship. Polygons also have diagonals, which are segments that join two vertices but no sides. It explains further about vertex of a polygon, sides of a polygon and the angles formed by it. E.g. A vertex is an endpoint of a line segment that forms a polygon. The line segments which form a polygon are called its sides and the angles formed by the line segments are known as the interior angles of a polygon. Polygons are named according to the number of sides and angles they have. For example, Triangle: 3 sides and 3 angles, Quadrilateral: 4 sides and 4 angles, Pentagon: 5 sides and 5 angles etc. In hexagon

*ABCDEF*, the vertices are

*A*,

*B*,

*C*,

*D*,

*E*and

*F*, the sides are

*AB*,

*BC*,

*CD*,

*DE*,

*EF*,

*FA*, and the angles are

*A*,

*B*,

*C*,

*D*,

*E*and

*F*.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

### Classifying Polygons

**Description:**

In this section you'll learn with the help of several examples about the classification of polygons. Polygons are primarily classified according to the number of sides and angles. The number of angles in a polygon always equals the number of sides. E.g. a triangle has 3 sides and 3 angles; a quadrilateral has 4 sides and 4 angles etc. If all the sides and interior angles of a polygon are congruent; then the polygon is a regular polygon, otherwise it is an irregular polygon. Regular polygons can be inscribed by a circle such that the circle is tangent to the sides at the centers, and circumscribed by a circle such that the sides form chords of the circle. Regular polygons are named to indicate the number of their sides or number of vertices present in the figure. Thus, a hexagon has six sides, while an octagon has eight sides. Further, the polygons may be characterized by their degree of convexity i.e. A polygon with no diagonal with points outside the polygon is called a convex polygon and a polygon with at least one diagonal with points outside the polygon is called a concave polygon.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

**Last Updated:**

**Subject(s):**- Mathematics
- Mathematics > Geometry

**Educational Level(s):**- Grades 9-10 / Ages 14-16
- Grades 11-12 / Ages 16-18

**Instructional Component Type(s):**- Curriculum: Lesson Plan

In this section you'll learn with the help of several examples about the classification of polygons. Polygons are primarily classified according to the number of sides and angles. The number of angles in a polygon always equals the number of sides. E.g. a triangle has 3 sides and 3 angles; a quadrilateral has 4 sides and 4 angles etc. If all the sides and interior angles of a polygon are congruent; then the polygon is a regular polygon, otherwise it is an irregular polygon. Regular polygons can be inscribed by a circle such that the circle is tangent to the sides at the centers, and circumscribed by a circle such that the sides form chords of the circle. Regular polygons are named to indicate the number of their sides or number of vertices present in the figure. Thus, a hexagon has six sides, while an octagon has eight sides. Further, the polygons may be characterized by their degree of convexity i.e. A polygon with no diagonal with points outside the polygon is called a convex polygon and a polygon with at least one diagonal with points outside the polygon is called a concave polygon.

### Interior and Exterior Angles of Polygons

**Description:**

In this mini-lesson, you will learn with the help of some examples and video presentation about the interior and exterior angles. Any polygon has as many corners as it has sides. Each corner has several angles and the two most important ones are- interior angle and exterior angle.

It explains how to find sum of all the interior angles and exterior angles of a polygon. An exterior angle of a polygon is the angle formed by any side and a line extended from an adjacent side. E.g. if the interior angle of triangle is 30° then its exterior angle is 150°. The sum of interior angles of a triangle is 180°, therefore, in case of isosceles right triangle the degree of angle measure would be 45°, 45°, and 90°. Take case of pentagon, which can be formed by joining three triangles and thus sum of interior angles is (3*180° = 540°). Thus each interior angle of a regular polygon is 108°.

Remember the fact that if the number of sides of a polygon is increased by 1, sum of the interior angles is increased by 180°. According to Polygon Interior-Angle-Sum theorem, sum of the measures of the interior angles of a polygon with n sides is equal to (n-2)180°. For example, sum of interior angles of a triangle is (3-2)180°, it comes to 180°. In general, interior angle of a regular polygon with n sides is given by: (n-2)180°/n. For example, the interior angle of a regular hexagon can be worked out by (6 - 2)180°/6 = 120°. Similarly the according to exterior Angle-Sum Theorem, the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. Remember also the exterior angle is the supplementary angle to the interior angle.

**Last Updated:**

**Subject(s):**- Mathematics
- Mathematics > Geometry

**Educational Level(s):**- Grades 9-10 / Ages 14-16
- Grades 11-12 / Ages 16-18

**Instructional Component Type(s):**- Curriculum: Lesson Plan

In this mini-lesson, you will learn with the help of some examples and video presentation about the interior and exterior angles. Any polygon has as many corners as it has sides. Each corner has several angles and the two most important ones are- interior angle and exterior angle.

It explains how to find sum of all the interior angles and exterior angles of a polygon. An exterior angle of a polygon is the angle formed by any side and a line extended from an adjacent side. E.g. if the interior angle of triangle is 30° then its exterior angle is 150°. The sum of interior angles of a triangle is 180°, therefore, in case of isosceles right triangle the degree of angle measure would be 45°, 45°, and 90°. Take case of pentagon, which can be formed by joining three triangles and thus sum of interior angles is (3*180° = 540°). Thus each interior angle of a regular polygon is 108°.

Remember the fact that if the number of sides of a polygon is increased by 1, sum of the interior angles is increased by 180°. According to Polygon Interior-Angle-Sum theorem, sum of the measures of the interior angles of a polygon with n sides is equal to (n-2)180°. For example, sum of interior angles of a triangle is (3-2)180°, it comes to 180°. In general, interior angle of a regular polygon with n sides is given by: (n-2)180°/n. For example, the interior angle of a regular hexagon can be worked out by (6 - 2)180°/6 = 120°. Similarly the according to exterior Angle-Sum Theorem, the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. Remember also the exterior angle is the supplementary angle to the interior angle.