AB is used to represent a line that connects two points A and B. It stretches endlessly in both directions. As a result, it can have an infinite number of points.

A line segment is a section of a line that is bound by two end points and contains every point on the line between them. Both ends are included in a closed line segment, whereas both end points are excluded in an open line segment. The sides of a triangle or a square are examples of line segments. More generally, when both end points of a line segment are vertices of a polygon or polyhedron, the line segment is either an edge (that of a polygon or polyhedron) or a diagonal. A chord is a line segment whose endpoints are both on a curve (such as a circle).

Parallel lines are defined as two or more lines that are on the same plane but never intersect. They have the same slope and are equidistant from one another. Pairs of angles are created when two parallel lines are intersected by a transversal line. While certain angles are complementary, others are congruent.

Do you know what a polygon is? Polygons are all around us! Polygons make up most of the shapes you see or study daily. A polygon is what you perceive when you see a rectangular wall.

Class 6 Maths Chapter 4 of NCERT has an easy explanation of a polygon:

Polygons are simple figures or forms built entirely of line segments. A polygon is the front view of a dice with a square shape. A polygon is formed by a pizza slice, which is triangular in shape. In mathematics, a polygon is defined as a closed two-dimensional structure, which is made up of line segments but not curves. 

 

The word polygon is derived from two Greek words: ‘poly’ (which means many) and ‘gon’ (which means angles). Triangles, rectangles, and squares are the three common types of polygons. 

 

On the basis of sides and angles polygons are categorised as:

 

• • Regular polygon

  • Irregular polygon

  • Convex polygon

  • Concave polygon

Regular polygon: In a a regular polygon the interior angles are all same. The sides are of the same length too. Regular polygons come in different shapes and sizes.

Irregular polygon: A polygon with irregular angles and side lengths is known as an irregular polygon.

Convex polygon: A polygon with all the interior angles less than 180 degrees is a convex polygon. Its vertex always faces away from the centre.

Concave polygon: A concave polygon is one that has one or more interior angles that are greater than 180 degrees.

In geometry, it is crucial to understand shapes. Shapes exist in a myriad of real-life situations.

 

Consider the following scenario where we come across polygonal shapes in different forms:

 

• • You walk on tiles that are square in shape

  • The truss (a framework of beams) of a building is triangular in shape 

  • The walls of a building are rectangular in shape 

  • Road signs have polygonal shapes

  • The portion of the chair on which you sit is rectangular in shape

  • The screen of your laptop, television, or mobile phone are all rectangular in shape.

  • The football pitch or playground is rectangular in shape

In geometry, a triangle is defined as a closed two-dimensional diagram with three sides, three angles and three vertices. In simple terms, a triangle is a three-sided polygon. 

 

The word triangle is derived from the Latin word ‘triangulus’, which means having three sides or three corners. In ancient times, astronomers developed a method called triangulation to calculate the distances between the stars. They measured the distance between two points in the sky and the angle generated by the observer’s movement or displacement between the two points called parallax. The Law of Sines was used to figure out how far they needed to go.

 

Around 2900 BC, the Egyptians built the pyramids. Pyramids are three-dimensional in shape with triangular faces. It was built with perfection with the same lengths and

angles on all sides. This technique was adopted by Greek mathematician Miletus (624 BC - 547 BC). Greek mathematician Aristarchus (310 BC - 250 BC), also employed the method to calculate the distance between the Earth and the Moon. Eratosthenes (276 BC - 195

BC) used the same approach to calculate the distance around the Earth's surface

(or earth’s circumference).

The concept of a triangle is very important in geometry. It has been used by mathematicians for ages to solve many problems. The properties of a triangle are extensively used in Euclidean geometry and trigonometry. 

 

Class 6 Maths basic geometrical ideas explain it well.

 

A triangle's main characteristics are as follows:

 

• A triangle is a two-dimensional polygon.

• A triangle is made up of three sides, three angles, and three vertices.

• The sum of the lengths of any two sides is greater than the length of the third side.

• The perimeter of a triangle is calculated by adding the lengths of its three sides.

• The product of the base and the height, divided by half equals the area of a triangle.

 

On the basis of the size of their interior angles, triangles can be divided into three groups:

 

• • Acute-angled triangle

  • Obtuse-angled triangle

  • Right-angled triangle

 

Acute-angled triangle: A triangle with all three interior angles less than 90 degrees is called an acute-angled triangle. 

 

Obtuse-angled triangle: In an obtuse-angled triangle one of the interior angles is greater than 90 degrees.

 

Right-angled triangle: A right-angled triangle is one in which one of the angles is 90 degrees. The longest side of a right-angle triangle is called the hypotenuse.

 

On the basis of the lengths of their sides, triangles can be classified into three categories:

 

• • Scalene 

  • Isosceles 

  • Equilateral

 

Scalene triangle: A scalene triangle is one in which all the sides are of unequal lengths and all the interior angles are of different angles measurements as well.

 

Isosceles triangle: An isosceles triangle is a triangle with two equal sides and two angles that are equal. Making an arc on each side of the triangle shows equal lengths.

Equilateral triangle: All three sides of an equilateral triangle are equal, as are all three interior angles. Each interior angle of an equilateral triangle is 60 degrees. An equilateral triangle is also known as an equiangular triangle as all three interior angles are equal.

The chapter Basic Geometrical Ideas is important in understanding mathematics as it is used as a basic concept in mathematics, physics and in every other aspect of the numerical and quantitative aptitude domain. So, the concepts must be crystal clear at an early stage of education.