Lines and Angles

Basics of Geometry

Do you want to know what Geometry is? This word is actually derived from the Greek word ‘geometron’. Now, ‘geometron’ is actually made of two words – Geo and Metron. So geometry is the mathematical study of all shapes and figures. It can be seen everywhere in our everyday life. We live in a world of shapes and here we shall see how mathematics helps us understand the basics of geometry. Let us study this topic in detail.

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Basics of Geometry

Let us see some basics concepts of geometry. Let start it right away with the general terms frequently used in the basics of geometry.

What is a Point?

A point is an exact location on the plane. It has no size. It is denoted by the capital letter of the English alphabet.

Collinear and Non- Collinear Points

Points which lie on the same straight line are collinear points. The points which don’t lie on the same straight line are non-collinear points.

Ray

Now we will discuss what is meant by a ray.  What comes to your mind when you think of the ray? Sun rays right? We know that the sun rays start from the sun and goes on endlessly. That means it has the starting point but it has no endpoint. So this nothing but a  ray.

Basics of Geometry

                                                                                                                                                 [Source: Shmoop]

The above figure shows what a ray is. A ray is nothing but a portion of a line. As the ray goes on endlessly, we cannot locate its end point. Let us name one of point as E. For the next point, we will just locate a point on the ray, say point F. So the name of the ray is ray EF.

Line

A line is a straight path that is endless in both directions. That means it extends in both directions without end.

Line Segment

A line segment is a part of a line. The main difference the line and the line segment is that lines do not have endpoints while line segments have endpoints.

Plane

The plane is a two-dimensional surface. A plane has length and width, but no height, and extends infinitely far on all sides. It is made up of made up of an infinite amount of lines.

Midpoint

A midpoint of the segment is the point that divides the segments into two congruent segments.

Angles

Basics of Geometry

Angle is the combination of two rays with a common endpoint. The symbol for an angle is ∠. The corner point of an angle is called the vertex of an angle.  The two straight sides of the angle are the arms of the angle.

Parallel lines

Basics of Geometry

When the distance between a pair of lines is always the same, then we call such lines as parallel lines.

Intersecting Lines

Lines that intersect each other at one point are something we call as intersecting lines.

You can find our detailed article on Geometry here.

Solved Examples for You

Question: If line l, m and n are such that l || m and m || n, then:

Basics of Geometry

  1. l || m
  2. line l ⊥ n
  3. l and n are intersecting
  4.  line l = n

Solution: The correct option is A. Lines m and n are parallel to each other and hence they are making an angle of 0° between them. In the same way, m and n are parallel to each other and they are making an angle of 0° between them. Therefore, angles between lines l and n is also  0° which proves l || n.

Question: An angle which measures 180° is called:

  1. Zero
  2. Right
  3. Straight
  4. acute

Solution: The correct option is C. An angle whose measure is exactly 180° is a straight line.

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