The Fundamentals of Geometry

The Basics of Geometry

Geometry is a significant branch of math that involves shapes, sizes, diagrams and angles. It has many practical applications. Its roots can be traced to ancient civilizations.

The ancient Greek mathematician Euclid coined the term geometry and systematically arranged the subject under a set of postulates and theorems that we still follow today.

Points

The field of geometry studies points, lines and planes in two dimensions. Geometry also includes the study of three-dimensional solid shapes like spheres, cubes, cones, prisms and pyramids.

The discipline of geometry, along with arithmetic, is one of the oldest branches of mathematics. Its development dates back to ancient times, with Euclid’s logical system codified in his Elements around 300 bce.

Modern geometry encompasses many subfields including analytic and synthetic geometry, differential and algebraic geometry. It also explores the properties of curved surfaces in spherical and hyperbolic geometry. Mensuration in geometry includes the calculation of perimeter, area and capacity of plane shapes, and the volume of solids.

Lines

A line is a one-dimensional geometric figure with length but not width. It extends infinitely in either direction and has no endpoints. There are many different types of lines. Some are straight and others are curved.

Two lines that are perpendicular to each other are called parallel lines. The perpendicularity of lines is very important in geometry, as it allows for the construction of right angles. Many geometric operations, such as finding the slope of a line, depend on this property.

A line segment is a section of a line that has a definite starting point and ending point. The points on the line that are at the same distance from the starting point are called collinear points.

Planes

A plane is a flat surface that has one dimension, length. Any two non-collinear points that are not parallel to each other must be on separate planes. They can intersect along a line.

Points, also known as points of coordinates, are a fundamental concept in geometry. They are represented by a dot and are named using capital letters. Points do not have height or width, so they are non-dimensional.

A plane is a mathematical space that has both affine properties and metrical properties induced by a coordinate system. Points in the plane can be specified uniquely by their ordered pair of coordinates, which are the signed distances from a point to the perpendicular lines that intersect it.

Angles

Angle measurement is a critical concept that engineers use to construct buildings, bridges, houses etc. Athletes and artists also use this concept to enhance their performance.

In geometry, an angle is a figure formed by two rays that share a common endpoint (also called the vertex of the angle). There are 7 types of angles: Acute angle, Obtuse angle, Right Angle, Reflex angle, Complete angle and Straight angle.

Each of these angles has a set of measurements that are unique to that type of angle. You can identify an angle by its measurements and name it based on its shape and direction. This knowledge is required for all geometry questions, including those in competitive exams like GMAT and CAT.

Polygons

Children will extend their knowledge of multi-sided shapes by learning about polygons. A polygon is a flat two-dimensional shape with straight sides that are connected to form a closed shape and have vertices (corners).

Children learn about regular and irregular polygons, including equilateral triangles and squares. They will use their knowledge of angles and sides to distinguish between the different types of polygons.

They will identify that a regular polygon has equal sides and angles, while an irregular polygon does not. They will also be taught how to find the perimeter of a polygon based on its number of sides. They will then learn about the interior and exterior angles of a polygon.

Circles

In geometry circles are closed curves with all points equidistant from a special point called the center. A circle has a lot of properties that make it interesting and unique.

One property is that tangents to a circle touch it at just one point. Two tangents drawn from the same point to the circle at different angles are equal (AM = MB).

A line segment that joins two points on the circumference of a circle is called a chord. Not every chord is a diameter, but every diameter satisfies the definition of a chord. Angles subtended by a chord are called inscribed angles. A circular region bounded by two radii is a sector.

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