Questions and Answers
What is the minimum number of sides a polygon can have?
What is the sum of the exterior angles of a polygon?
What is the sum of the interior angles of a quadrilateral?
What is the name of a 100-sided polygon?
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What is an interior angle of a polygon?
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What is the sum of the interior angles of a heptagon?
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What is the main difference between a regular and irregular heptagon?
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What is the sum of the interior angles of an octagon?
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What is a common real-world example of a regular octagon?
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What is a characteristic of a regular polygon?
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What is the primary difference between a polygon and a regular polygon?
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What is the name of a regular polygon with five sides?
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What is true about the interior angles of a regular triangle?
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Why is a circle not considered a polygon?
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What is the sum of the exterior angles of a polygon?
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Study Notes
What is a Polygon?
- A polygon is a flat, solid shape with only straight sides, no curved sides, and no gaps in the sides.
- Polygons can be laid side to side with other polygons to form a larger shape without gaps or spaces.
- The minimum number of sides a polygon can have is three, and there is no maximum number of sides.
Types of Polygons
- A three-sided polygon is called a triangle.
- A four-sided polygon is called a quadrilateral.
- Polygons with specific numbers of sides have unique names (e.g., pentagon with five sides, hexagon with six sides, heptagon with seven sides, octagon with eight sides).
- If the name of the polygon is not known, it can be referred to as an n-gon, where n represents the number of sides.
- A 100-sided polygon is called a hectogon.
Angles in Polygons
- The exterior angles of any polygon always add up to 360 degrees.
- The interior angles of a polygon add up to 180 degrees for triangles, 360 degrees for quadrilaterals, and an additional 180 degrees for each additional side.
- An interior angle is an angle between two adjacent sides that is inside the shape.
- An exterior angle is the angle outside the shape formed by extending a side beyond the shape.
- When an interior angle is added to its adjacent exterior angle, the sum is always 180 degrees, forming a straight line.
Regular Polygons
- A regular polygon is a polygon whose sides are all the same size and whose interior angles are also all the same size.
- All regular polygons are polygons, but not all polygons are regular polygons.
- A regular polygon has all sides of equal length, and all interior and exterior angles are the same measurement.
- Examples of regular polygons include an equilateral triangle, a square, and regular polygons with more sides.
Parts of a Polygon
- A polygon has straight sides that connect with each other, with no gaps or curved sides.
- All the sides in a polygon connect with one another, forming sharp corners wherever two sides connect.
- Polygons with four sides or more will have diagonals, which are straight lines that can be drawn between corners connecting them inside the shape.
Types of Regular Polygons
- For each type of polygon, a regular polygon exists that has the same number of sides with each side being the exact same length as every other side and with all interior angles measuring the same.
- Examples of regular polygons include an equilateral triangle, a square, regular pentagons, regular hexagons, and so on.
Is a Circle a Polygon?
- A circle is not a polygon because its sides are not straight, but rather a continuous curve that connects back to itself.
- Any shape with curved sides is not a polygon, including crescents and half circles.
Heptagon and Octagon
- A polygon of 7 sides is called a heptagon or septagon, with the sum of its interior angles being 900 degrees and the sum of its exterior angles being 360 degrees.
- A polygon of 8 sides is called an octagon, with the sum of its interior angles being 1080 degrees and the sum of its exterior angles being 360 degrees.
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Description
Learn about the definition and properties of polygons, including their straight sides and lack of gaps. Discover the minimum number of sides a polygon can have.
