Understanding the Basics of Geometry

A Beginner’s Guide to Geometry

Geometry is a branch of mathematics that studies the properties of shapes. It includes planes, lines, angles and solids. It also deals with the relationships between them.

Children need to learn the names of the geometric shapes, as they will use them in many problems. A line is straight if it extends in both directions without end (infinitely). An angle is a figure with two rays sharing a common point called the vertex.

Planes

The Greek mathematician Euclid developed the concept of planes, along with a number of other fundamental concepts, which form the basis for all geometry that comes after him. All two-dimensional geometry is based on the idea of a plane, which is flat and extends infinitely into space without any height or width.

As a noun, “plane” can mean an airplane or a tool for smoothing wood, but it’s also used in mathematics to refer to any flat figure. Renaissance artists also helped lay the groundwork for plane geometry through their techniques of drawing in perspective.

Any three points that don’t fall on a single line are on one plane, and any two intersecting planes are always parallel to each other. The XY plane, shown below, is an example of an intersecting plane.

Polygons

In geometry, a polygon is a flat, plane, closed shape with straight sides that do not intersect each other. The angles of a polygon must be equal and measure less than 180°. A regular polygon is a convex figure.

Each side of a polygon connects to two or more vertices. A polygon can have a variety of sides, but the sides must be non-intersecting. A triangle is a simple polygon with three sides. A quadrilateral is a four-sided polygon, a pentagon has five sides, and a hexagon has six sides.

Each interior angle of a regular polygon is equal to 180°, and each exterior angle is 360°. Polygons have different names depending on the number of sides they have. If a polygon has n sides, it is called an n-gon.

Angles

Angles are a key concept in geometry. They help us build better streets and cities, tell time using shadows and sunlight, and even understand our solar system.

There are two main parts to an angle: the vertex and the arms. The vertex is the corner point of an angle, where two rays meet. The arms are the two sides of an angle, joined at a common endpoint. For example, in the given figure, OA and OB are the two arms of the angle.

Adjacent angles are those that share a vertex and a side but don’t overlap with one another. Supplementary angles are those whose sum is equal to 180 degrees. Alternate exterior angles are pairs of angles that appear on the outsides of parallel lines and on opposite sides of a transversal.

Lines

Lines are one-dimensional figures that are straight and extend forever in opposite directions. They are often seen in many 2D shapes and real world items. A line is made up of many different parts called vertices.

Students will first learn about lines as part of geometry in 4th grade. They will learn about the types of lines and how they are classified. They will also learn about the relationship between a line, a line segment and a ray.

It is important to understand the difference between a line and a line segment. A line has no endpoints, while a line segment has a definite beginning and an end. You may see the latter in a length of string or on a piece of paper.

Circles

In geometry, a circle is a 2D shape which has a radius. It is a locus of points that are equidistant from a common point (the centre of the circle).

Two circles are called congruent if their centres are at the same distance apart. Equal chords of a circle are always equidistant from the centre and the perpendicular bisector of a chord passes through the centre of the circle.

A circle can be split into parts based on their position. A segment of a circle created by a chord is also known as an arc. It can be divided into major and minor arcs. A sector of a circle is the area enclosed by two radii and their corresponding arcs. It can be divided into two types – minor sector and major sector.

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