FUNDAMENTAL CONCEPT OF GEOMETRY -
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.
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.
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).
A surface has length and width, but no thickness.
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.
An angle is formed when two rays share a common endpoint. The degree of rotation between the rays measures the angle.
These are closed geometric shapes with straight sides. Common polygons include triangles, quadrilaterals, pentagons, and hexagons.
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.
Triangles are three-sided polygons. They have various classifications based on their angles (acute, obtuse, right) and side lengths (equilateral, isosceles, scalene).
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.
These include translations, rotations, reflections, and dilations, which change the position, orientation, or size of geometric figures.
The property of figures that remain unchanged when they are flipped, rotated, or reflected.
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.