# NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5

Free NCERT Solutions for Class 6 Maths Chapter 4 Exercise 4.5 (Ex. 4.5) Basic Geometrical Ideas in PDF format, download to use it offline or online, any time everywhere. Class 6 Maths PDF Solutions as well as Videos solutions are updated for current academic session 2020-2021 using step by step calculations.

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Class: 6 | Mathematics |

Chapter: 4 | Basic Geometrical Ideas |

Exercise: 4.5 | English Hindi Solutions |

### CBSE NCERT Class 6 Maths Chapter 4 Exercise 4.5 Solution in Hindi and English Medium

### Class 6 Maths Chapter 4 Exercise 4.5 Solution in Videos

##### Ray

We are aware of the fact that the sun emits rays of light. Also, a lighted tourch emits rays of light. Even an eye emits rays of light.

A ray of light originates from a point in the sun or from the bulb of the tourch and extends endlessly in a certain direction.

Thus, a ray starts from a fixed point and extends endlessly in a given direction.

###### Important Facts About a Ray:

(i) A ray is a part of a line.

(ii) A ray has only one end-point known as initial point.

(iii) A ray extends endlessly in a given direction.

Note: Just as we cannot draw the whole of a line, we cannot draw the whole of a ray on paper. We shall, therefore, refer to a part of a ray as a ray.

##### Properties of Rays

(i) Since an unlimited number of lines can pass through a given point, so, an unlimited number of rays can be drawn with a given point as the initial point.

(ii) Since a unique line can be drawn passing through two different given points in a plane, so, there is a unique ray with O as initial point and passing through a given point P. We call this as ray OP. It is written as OP and read as ray OP.

Ray OP means that the ray starts from the initial point O and passes through P extending indefinitely in the direction from O to P.

Thus, a ray is completely known if its initial point and one more point on it are known.

Note: We know that there is no difference between line AB and line BA. Also, line segment AB is same as the line segment BA. But, ray OP and ray PO are different rays. Ray OP extends indefinitely in the direction from O to P, while ray PO extends indefinitely in the direction from P to O. In fact rays OP and PO are called opposite rays.

##### What is the relationship between lines segments and rays?

You can measure the length of a segment, but not of a line. A segment is named by its two endpoints, for example, AB. A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

##### Does every ray contain a line segment?

Yes, every ray will contain a line segment because a ray has two points it starts with an end point then it goes beyond the other point, and a line only needs two points to define it and it lies between them therefore every ray has two points to contain a line segment.

##### How many rays are in a line?

Note that a line segment has two end-points, a ray one, and a line none. An angle can be formed when two rays meet at a common point. The rays are the sides of the angle. The point of the end of two rays is called the vertex.

##### How do you count Rays?

In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is, each of our rays must begin with. Only fails to do so.