Plane Shapes - Definition, Types, Examples, Facts, FAQs (2024)

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What Are Plane Shapes?

In geometry, plane figures or plane shapes, also known as two-dimensional shapes, are fundamental geometric figures that exist in a flat, two-dimensional plane.

Plane shapes do not have thickness or depth unlike three-dimensional shapes, making them ideal for representation on a flat surface, such as a piece of paper. These shapes are the building blocks of geometry and are extensively studied in mathematics.

Definition of Plane Shape

Plane shapes can be defined as two-dimensional geometric figures that exist on a flat surface, known as a plane.

These shapes have only length and width, with no depth or thickness. They are characterized by their boundaries, which can be made up of straight sides or curved lines. Plane shapes examples include polygons (triangles, quadrilaterals), circles, and other curvilinear figures.

Different Plane Shapes in Geometry

In geometry, there are several different types of plane shapes. Here are some of the most commonly discussed ones:

Triangles	Triangles are closed plane shapes with three sides and three angles.
Quadrilaterals	Quadrilaterals are closed plane shapes with four sides and four angles. Common examples are squares, rectangles, and parallelograms.
Circles	Circles are plane shapes with a curved boundary consisting of all points equidistant from a fixed point called the center.
Ovals	Oval shape is a plane shape that resembles the shape of an egg or a squashed circle.
Different Polygons	Polygons are closed plane shapes with at least three sides. Polygons with three sides: TrianglesPolygons with four sides: QuadrilateralsPolygons with five sides: PentagonsPolygons with six sides: Hexagonsetc.

What Are Open and Closed Shapes?

In geometry, plane shapes can be categorized as open or closed based on their boundaries.

1. Closed Plane Shapes: Closed shapes are plane figures that have a complete and continuous boundary that forms a closed loop. This means that the shape does not have any openings (holes) or breaks in its boundary.

Examples of closed plane shapes include polygons (such as triangles, squares, pentagons), circles, ellipses, etc. These shapes enclose a finite area within their boundaries.

2. Open Plane Shapes: Open shapes are figures that do not have a complete and continuous boundary. They have one or more openings or breaks in their boundary, which means they do not form a closed loop.

Examples of open plane shapes include lines, line segments, rays, and curves that do not form closed loops (like a curve with endpoints that do not meet). Open plane shapes do not enclose any area since they lack a complete boundary.

Polygons

Polygons are most commonly discussed plane shapes apart from circles.

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with at least three sides.

It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.

The types of polygons can be categorized into three major forms: regular or irregular, concave or convex, and simple or complex.

Regular Polygons and Irregular Polygons:

Regular Polygons	Irregular Polygons
A regular polygon has all sides of equal length and all interior angles of equal measure. Examples include equilateral triangles, squares, and regular pentagons.	An irregular polygon has sides of different lengths and/or interior angles of different measures. Examples include scalene triangles, rectangles, and irregular hexagons.

Convex Polygons and Concave Polygons:

Convex Polygons	Concave Polygons
A convex polygon has all its interior angles less than 180 degrees. All sides of a convex polygon lie on the same side when any two points inside the polygon are connected. Examples include equilateral triangles, squares, and regular hexagons.	A concave polygon has at least one interior angle greater than 180 degrees. It has at least one “caved-in” or “dented” portion. Examples include a star shape or a crescent shape.

Simple Polygons and Complex Polygons

Simple Polygons	Complex Polygons
A simple polygon is non-self-intersecting, meaning that its sides do not cross over each other. It forms a single continuous shape. Examples include triangles, rectangles, and regular polygons.	A complex polygon is self-intersecting, meaning that it has sides that cross over each other, creating additional interior regions within the polygon. Examples include shapes with holes or overlapping sides.

Sides and Vertices of Plane Shapes

Sides: In plane shapes, the sides refer to the straight line segments that form the boundary of the shape.

Vertices: The corners or the points where the sides meet are called the vertices.

It’s important to note that some plane shapes, such as circles, do not have straight sides or corners/vertices. Instead, they have a continuous curved boundary. However, polygons are the plane shapes that have distinct sides and corners/vertices that define their structure.

No sides, No Corners

Plane Shapes vs. 3D Shapes

Facts about Plane Shapes

Conclusion

In this article, we have learned about plane shapes. Learning about plane shapes provides a solid foundation for geometry, enhances problem-solving skills, and has practical applications in numerous fields. It promotes critical thinking, spatial reasoning, and effective communication, making it both useful and necessary in education and beyond. Now let’s solve some examples and practice problems for better understanding.

Solved Examples on Plane Shapes

Example 1: Classify the following plane shape as open, closed, simple, or complex.

Solution:

The shape crosses itself.

So, it is not simple. It is a complex shape.

It forms a closed loop.

So, it is a closed shape. It is not an open shape.

Example 2: Which of the following are not plane shapes?

Circle, Sphere, Cube, Square, Cuboid, Triangle

Solution:

Sphere, cube, cuboid are 3D shapes or geometric solids.

So, they are not plane shapes.

Circle, square, triangle are plane shapes.

Example 3: Which of the following is not an open shape?

Solution:

Shapes a, b, and c have different starting and end points. They do not have any interior.

The shape d does not have any open ends, so it is a closed shape. It forms a closed loop and has an interior.

Example 4: How many sides, vertices does this shape have? Is the shape closed or open?

Solution:

First, we count the number of straight line segments in the shape.

There are eight straight lines connected to each other, making an octagon.

As this octagon’s outline may be traced without any gaps, it is a closed shape.

Practice Problems on Plane Shapes

Frequently Asked Questions about Plane Shapes