📘 Chapter 2 – Lines and Angles
Textbook Page 10 Explanation
This page explains collinear points, non-collinear points, and plane.
📍 Collinear and Non-collinear Points
💬 Mathematical Discussion
(1) “Take a point on a paper. Draw lines passing through it. How many such lines can be drawn?”
(2) “Now take two points on a paper. Draw lines passing through both points. How many such lines can be drawn?”
(3) “Take three points on a paper. How many lines can be drawn through all three points?”
These questions help us understand how many lines can pass through one point, two points, and three points.
Through one point, many lines can be drawn.
Through two points, only one line can be drawn.
Through three points, one line can be drawn only if all three points lie on the same straight line.
👧 Sarita's Points
“Sarita and Afroz drew those three points as follows.”
Sarita drew three points named A, B and C. These three points are in one straight line.
“Only one line can be drawn through all three points drawn by Sarita.”
This means points A, B and C are lying on one straight line. So, one line can pass through all three points.
“If a single line passes through three or more such points, they are called collinear points.”
So, collinear points are points that lie on the same straight line.
Example: If points A, B and C are all on one straight line, then A, B and C are collinear points.
👦 Afroz's Points
Afroz drew three points named P, Q and R. These points are not in one straight line.
“No line can be drawn that passes through all three points drawn by Afroz.”
This means points P, Q and R do not lie on the same straight line. So, one single line cannot pass through all of them.
“If a line cannot be drawn through three or more such points, they are called non-collinear points.”
So, non-collinear points are points that do not lie on the same straight line.
Example: If P, Q and R are placed in different positions and no single straight line can pass through all three, then they are non-collinear points.
🐦 Birds Seated on a Cable
“Birds seated on a cable”
The textbook shows birds sitting on a cable.
When birds are sitting on the same straight cable, their positions are like collinear points.
If one bird is not sitting on the cable and is flying away, then all the bird positions are not on one straight line. So they are like non-collinear points.
Birds sitting on the same straight cable show collinear points.
Birds not lying on the same straight line show non-collinear points.
▭ Plane
“The surfaces of a table and board in the picture are flat. These flat surfaces are parts of a surface that is infinite on all sides. A flat surface that is infinite on all sides is a plane. This boundless is shown by arrows. The name of a plane is indicated by a capital letter in English, such as plane E.”
A plane is a flat surface that extends endlessly in all directions.
The top surface of a table and the surface of a board are flat. These are small parts of a plane.
In geometry, a plane is imagined as a flat surface that has no boundary. It goes on endlessly on all sides.
Arrows are used in the diagram to show that the plane continues endlessly.
A plane is named by a capital letter. In the textbook figure, it is called plane E.
“Point, line and plane are basic concepts in geometry.”
🌟 Page Summary
- Through one point, many lines can be drawn.
- Through two points, only one line can be drawn.
- Three or more points lying on one straight line are called collinear points.
- Three or more points not lying on one straight line are called non-collinear points.
- A plane is a flat surface that extends endlessly in all directions.
- A plane is named using a capital letter, like plane E.
- Point, line and plane are basic concepts in geometry.