📘 Chapter 2 – Lines and Angles
Textbook Page 9 Explanation
This page introduces the basic ideas of point, line and plane with the help of a kabaddi field.
🔁 Revision
“Geometric shapes and basic concepts are used in designing any playground. The adjacent picture shows a kabaddi field being designed. Some basic geometric concepts have been used in designing it, such as point, line and plane.”
This means geometry is not only in books. We can see geometry in real life too. A playground, a classroom, a road, a field and many other things are made using basic geometric ideas.
In the kabaddi field shown on the page, many straight lines are drawn. These lines help to mark different parts of the field. Points are also used where lines meet or where positions are marked.
“Now we will study the basic concepts: a point, a line, and a plane. These elements will help us understand the design and analysis of various shapes in geometry.”
In this chapter, we first learn about very basic things: point, line and plane. These are the building blocks of geometry. After understanding them, we can understand shapes, angles and diagrams more clearly.
📍 Point
“Place a sharp pencil on the paper and make a mark. This mark is a point. A point has no length, width or thickness. Capital letters in English are used to denote Points. For example, point P, point Q, point R.”
A point is a small mark made by a sharp pencil. It shows an exact position.
A point has no length, no width and no thickness. It only shows a location.
In geometry, points are named using capital letters like P, Q and R. So we say: point P, point Q and point R.
A dot on paper, a city marked on a map, or a small position marked in a diagram can be understood as a point.
🧭 Do it
“Indicate the following cities with points on the neighbouring outline map of Maharashtra.”
1) Pune 2) Mumbai
3) Nashik 4) Nagpur
5) Kolhapur 6) Satara
In this activity, students have to mark the given cities on the Maharashtra map using points. Each city is shown by one small dot or point.
This activity helps us understand that a point can show the exact place of something on a map.
📏 Line
“The figure below is a line. Line is infinite on both sides. To show this, arrow marks are drawn at both ends. Line is one-dimensional and there are an infinite number of points on a line.”
A line is straight and goes on endlessly in both directions. It does not stop.
To show that a line continues forever, arrow marks are drawn at both ends.
A line is one-dimensional. It has only length. It has no width and no thickness.
A line contains an infinite number of points. This means we can imagine countless points lying on a line.
“The name of a line is written by using any two points on the line. For example, the name of the line in the adjacent figure is line DE or line ED. Sometimes, the name of the line is also written using a single letter in the lowercase English script, such as line m, line n, line a.”
A line can be named using any two points on it. In the figure, the points are D and E. So the line can be called line DE or line ED.
Sometimes, a line is also named using a small English letter like line m, line n or line a.
📍 A point shows position.
📏 A line is straight and endless on both sides.
🔠 Points are named with capital letters like P, Q, R.
🔡 Lines may be named with two points like line DE or with a small letter like line m.
🌟 Page Summary
- Geometry is used in designing playgrounds like a kabaddi field.
- Point, line and plane are basic concepts of geometry.
- A point has no length, width or thickness.
- A point is named using capital letters.
- A line is infinite on both sides.
- A line is one-dimensional.
- A line can be named using two points or one small letter.