Polygon Curve Angle: Meaning & Types

Geometry is one of the major segments of mathematics that especially deals with study of shapes and sizes of different figures. It is widely classified into Plane geometry and Solid Geometry. Plane and Solid geometry varies from one another. When plane geometry deals particularly with flat structures, like polygons, curves, and lines and circles – solid geometry talks vividly about three-dimensional shapes, likespheres, cubes, cones, and more.

Read Also: Coordinate Geometry

Key Takeaways: Polygon, Curve, Angle, Obtuse angle, Acute angle, Reflex angle, Right angle, Regular polygon, Convex polygon, Concave polygon, Simple curve

What is a Polygon?

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A polygon simply is an enclosed geometric figure that has three or more straight line segments. Typically, the straight line segments that enclose the figure are collectively known as the sides of the polygon.

Polygon

In the above figure, AB is a side. While A, B, C, D and E are all vertices of the polygon shape. A and E make adjacent vertices, while A and C make non-adjacent vertices. Moreover, AC is a diagonal.

• Besides, the point at which two straight line segments gradually meet is otherwise known as the vertex. 
• Moreover, the pair of sides which eventually meet exactly at the same vertex are known as adjacent sides and the touchpoints of either side are widely also called adjacent vertices. 
• The diagonal of a polygon is its non-adjacent vertices.
• A regular polygon can be determined if the sides of it are equal in length. For instance, a square is a perfect epitome of the same. A rectangle is an irregular polygon.
• The minimum number of sides a polygon should have is three. And a perfect example of the same is a triangle.
• The nomenclature each polygon has is based on the number of sides it has. For example, a pentagon typically has five sides, while a square has four.

Check Important Notes for Centroid of a Triangle

Types of Polygon

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There are four major types of Polygons:

• Regular Polygon: A Polygon with equal sides and angles is known as Regular Polygon.
• Irregular Polygon: A Polygon with unequal sides and angles is known as an Irregular Polygon.
• Convex Polygon: A polygon that has the boundary of a convex set is known as Convex Polygon.
• Concave Polygon: A polygon that does not have the boundary of a convex set is known as Convex Polygon.

What is a Curve?

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A curve, if simply defined, can be anything but straight in shape. A curve is a non-straight line that bends or changes its direction at least about once.

Curve Shapes

It is usually a continuous, especially endless, line that changes directions. For example, mountainous roads are a prime instance of a curve. Many random lines that you have probably drawn until now fall under the category of a curve.

Check Also: Properties of Parallel Lines

Types of Curve

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There are several kinds of curves, like simple curves, open curves, and closed curves, upward curve, downward curve and non-simple curve.

• Open Curve: An open curve is typically a curve whose endpoints apparently do not meet. Closed curves, however, encloses a full area and does not have any endpoints.
• Upward Curve: An upward curve usually faces upwards in direction, and is also otherwise known as a concave curve. A downward curve, on the other hand, faces downwards in direction, and is usually also known as convex curve.
• Simple Curve: A simple curve doesn’t usually intersect itself at any particular point. A non-simple curve, however, is seen to intersect its own line of direction during movement.

What is an Angle?

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When two lines intersect very close to the point of meeting, it typically then creates a space (measured generally in degrees) which is known as an angle.

Angles

There are several parts of an angle, much like the vertex, interior angle, exterior angle and its arms. Two lines that usually intersect at a specific point causes the formation of four angles simultaneously during intersection. The symbol of an angle is ∠.

Check Also: Alternate Angles

Types of Angles

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Angles can be classified in many parts like, acute angle, obtuse angle, reflex angle and right angle. They are named and determined as per their shape and size.

• Acute Angle: An acute angle is formed when the measurement between the two main arms is less than 90 degrees.
• Obtuse Angle: An obtuse angle is typically formed when the measurement between the two main arms is more than 90 degrees.
• Reflex Angle: A reflex angle is formed when the measurement between the two main arms is usually more than 180 degrees, but less than 360 degrees.
• Right Angle: A right angle is formed when the measurement between the two main arms is exactly 90 degrees.

Points to Remember

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Following are some important points:

• A polygon is an enclosed geometric shape that has three or more straight line segments. One major example of a polygon is a triangle, which is also a figure that has the least number of sides a polygon is supposed to have.
• Regular Polygon, Irregular Polygon, Convex Polygon and Concave polygon are all types of polygon.
• A curve can be anything but straight in shape. A curve is a non-straight line that changes its direction at least about once.
• Simple curves, open curves, and closed curves, upward curve, downward curves, and non-simple curves are the major types of curves.
• Angles are categorized into four parts, like acute angle, obtuse angle, reflex angle and right angle.

Read More: Linear Pair Axiom