Concepts of geometry - basics(point, line, angle and parallel lines)

Geometry is everywhere around us, in man made structures, in nature, in sports, in art and in lots of more things. In geometry, we have 4 ideas or can also be said as imaginary things i.e. point, line, plane and space and everything else is built and based on the fundamentals of these concepts.

Let's go on with the concepts:

Point
A point is a location is space and it has absolutely no dimensions i.e. no length, no width and no depth. We use a dot, for example; point D or point E, to represent a point.

Line
A line is a set of points that has only 1 dimension, length. The arrowheads shows that it is extending in both the directions and has no end points. Hence it has no fixed length.

• Line segment: It is the part of a line that has a specific length and specific end points. 2 line segments having the same length are called congruent line segments.  
• Ray: It is the part of a line that has only one end point. It extends endlessly in one direction.

Two lines can be related to each other in 4 different ways:

1. Lines that have just one point in common are called intersecting lines.
2. Lines that lie in the same plane but never intersect even if produced endlessly in both directions are called Parallel lines.
3. Two intersecting lines that form a right angle are called Perpendicular lines.
4. Lines that are not in the same plane and do not intersect are called skew lines.

• Plane: The set of points all lying on one surface is called a plane. A wall, surface of a table, floor etc. are all examples of a plane. A plane actually extends endlessly and the surface of a plane has no thickness. At least three points not on the same line are needed to define a plane.

Angle

Two rays(to be precise) that share a common endpoint form an angle. The common endpoint is called the vertex.

Types of angles; 5 main types:

1. Straight angle: An angle measuring 180° is called a straight angle.
2. Acute angle: An angle whose measure lies between 0° and 90° is called an acute angle.
3. Obtuse angle: An angle whose measure lies between 90° and 180° is called an abtuse angle. 
4. Right angle: An angle whose measure is equal to 90° is called a right angle.
5. Reflex angle: An angle whose measure lies between 180° and 360° is called a reflex angle.

The above five are the main ones. But there are many more left.

• Complementary angles: 2 angles are known as complementary angles if the sum of their degree measures 90°.
• Supplementary angles: 2 angles are known as supplementary angles if the sum of their degree measures 180°.
• Adjacent angles: 2 angles having a common vertex and a common side (ray) are called adjacent angles.
• Linear pair: 2 adjacent angles form a linear pair if they are supplementary i.e., their sum is 180°.
• Angles at point: Sum of the angles round a point is 360°.
• Vertically opposite angles: They are the pairs of angles formed by 2 intersecting lines opposite to each other. They are always equal (or congruent).

Parallel lines

Lines in a plane which do not intersect are called parallel lines. A pair of parallel lines are always the same distance (perpendicular distance) apart.

Transversal: A line which intersects 2 or more given lines in distinct points is known as transversal to the given lines. The lines may be intersecting lines.