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FUNDAMENTAL CONCEPT OF GEOMETRY

__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.**

**(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**

**(ii) Line:- **

**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.**