Home The World of Plane Geometry

# The World of Plane Geometry

How can we define plane geometry? We know that geometry is one large branch of mathematics, but oftentimes people forget just how many subcategories there are within a topic like geometry. While geometry deals with points, lines, angles, solids, and surfaces, plane geometry is about flat shapes like lines, circles, triangles, and angles– any shape that can be drawn on paper.

However, on the other side of geometry is solid geometry which talks about three-dimensional objects in space. Objects like spheres, cubes, and cylinders exist in solid geometry because they have height, length, and width. Solids have properties like volume, surface area, and more. Not sure about the difference between all of these terms in geometry? Let’s dive into it and find out more.

## What’s the Difference?

In plane geometry, there are 3 key terms to understand that will help you along the way. A point, a line, and a plane are all the bases of plane geometry.

### Point

A point is simply a position or exact location. For example, if you draw a dot on a piece of paper, that is a point. It has no dimension to it but simply represents the exact location it is positioned at. Oftentimes, a point is labeled with a name like “A” or using coordinates on a graph. Cartesian Coordinates mark a point based on how far up and across a point is on said graph.

### Line

A line is straight, has no thickness, and goes on infinitely on both ends- so it has no ends! A line segment, however, does have two ends. A line with just one end is called a ray. Just like the ray from the sun, it starts on one end going in one direction infinitely.

### Plane

A two-dimensional (2D) shape has no thickness, but it does have length and width. A plane is made up of lines and thus goes on forever.

## Polygons

Many of the shapes in planes are called polygons. Polygons have straight sides, but sometimes not all sides are equal. The word “polygon” comes from the Greek language. Poly- means “many” and -gon means “angle”. Thus, polygon equates to “many angles”. It is also important to note that a polygon must have at least 3 sides.

A regular polygon has sides and angles that are all equal- like a triangle, square, pentagon, or hexagon… and so on. Other common polygons that are irregular are rectangles, parallelograms, trapezoids and more. These are not considered regular because all sides and angles are not the same. For example on a rectangle, 2 opposing sides are the same, but the other 2 opposing sides are different from the original 2.

We have talked about what a polygon does have, but what can a polygon not have? A polygon cannot have any curved sides or be open (meaning that it is fully enclosed and all lines meet). So a shape that might resemble the letter “C” could not possibly be a polygon due to the open side. A shape that resembles the letter “D” also cannot be a polygon due to the curved sides.

## Curved Shapes

Now that we have covered polygons – shapes with only straight sides – what do we do regarding shapes that are curved? A circle or even an oval are great examples of this. A circle is essentially a fully rounded line with each point along that line being equidistant to the center. There are no corners or edges in a circle. The word “circle” comes from the Greek word “kirkos” which means ring or hoop.

Length and width of a curved shape, like a circle, are a bit more complex than these properties when we are dealing with straight lines. Finding the length, width, and area of curved shapes requires that we know different equations. For example, since a circle is a round shape with no corners, the length and width are the same and are actually called the diameter. The diameter is the distance from any point on the circle across to the other side.

## At OMC

As you can see, plane geometry can be complex and contains many details that are crucial to know in order to then understand solid geometry. At OMC, we ensure that all students leave school with a solid education of math concepts such as geometry, and the ability to use the concepts that they have been taught in the classroom. Whether geometry comes naturally to a student or not, we offer classes and tutoring that can assist them in strengthening their foundation in mathematics. OMC strives to ensure every student reaches or surpasses their full potential.

Contact OMC today to help ensure your child gains a solid, complete understanding of the most important mathematical concepts, such as plane geometry, by signing them up for classes that are tailored to their specific educational needs.

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