Geometry is a branch of mathematics that deals with the study of shapes, sizes, properties of space, and the relationships between various objects in space. It's a fundamental concept in mathematics and has numerous real-world applications. Here are some fundamental concepts in geometry:-


Points, Lines, and Planes: These are the basic building blocks of geometry.

(i) Points:-

  • A point is a location in space, represented by a dot and having no dimension.
  • A point is a mark of position. It has neither length nor width nor. thickness and occupies no space. A point determines a location. It is usually denoted by a capital letter


A line has only length. It has neither width nor thickness. It is a one-dimensional figure having the following features:

1. It is straight (has no bends),

2. Has no thickness

3. And it extends in both directions without any end (could be extended infinitely from both ends).

4. A line is a straight path of points that extends infinitely in both directions.


(iii) Ray:-

It is a line (i.e. a straight line) that starts from a given fixed point and moves in the same direction.

A ray is a portion or part of a line which begins at a point (which cannot be extended any further) and goes off or extends in a particular direction to infinity.

The sun rays are a popular example as they initiate from a source point called sun and the rays extend to a particular direction till infinity.


(iv) Line Segment:-

A line segment is a part of a straight line. A line segment is a part of a line and also of a ray. A line segment refers to the shortest or the least distance between two points. The line segment joining two points say A and B are denoted by AB (bar).


(v) Surface:-

A surface has length and width, but no thickness.

(vi) Plane:-

It is a flat surface. A plane has length and width, but no thickness. A plane is a flat surface that extends infinitely in all directions.

(vii) Collinearity of Points:-

If three of more points lie on the same straight line, then the points are called collinear points.


(viii) Angles:-

An angle is formed when two rays share a common endpoint. The degree of rotation between the rays measures the angle.

(ix) Polygons:-

These are closed geometric shapes with straight sides. Common polygons include triangles, quadrilaterals, pentagons, and hexagons.

(x) Circles:-

A circle is a set of points in a plane that are equidistant from a central point. Circles have a constant radius and are defined by their diameter, circumference, and area.

(xi) Congruence and Similarity:-

Congruent shapes have the same shape and size, while similar shapes have the same shape but different sizes. These concepts are essential for comparing and analyzing shapes.

(xii) Triangles:-

Triangles are three-sided polygons. They have various classifications based on their angles (acute, obtuse, right) and side lengths (equilateral, isosceles, scalene).

(xiii) Quadrilaterals:-

Four-sided polygons, including rectangles, squares, parallelograms, trapezoids, and rhombi.

(xiv) Circles and Circular Geometry:-

Concepts related to circles include the circumference, diameter, radius, central angles, and arc length.

(xv) Area and Perimeter:-

Area measures the amount of space inside a shape, while perimeter measures the total length of its boundary.

(xvi) Coordinate Geometry:-

The use of coordinates to represent points and equations to describe lines and curves.

(xvii) Transformations:-

These include translations, rotations, reflections, and dilations, which change the position, orientation, or size of geometric figures.

(xviii) Symmetry:-

The property of figures that remain unchanged when they are flipped, rotated, or reflected.

(xix) Trigonometry:-

The study of relationships between the angles and sides of triangles. It has applications in measuring distances, heights, and angles in various fields.

(xx) Solid Geometry:-

The study of three-dimensional shapes, including prisms, pyramids, cylinders, cones, and spheres.

(xxi) Geometric Proofs:-

Using logical reasoning to demonstrate the validity of geometric statements and theorems.