Page 1 Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you. 4.2 Points By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. 4.1 Introduction Chapter 4 Chapter 4 Chapter 4 Chapter 4 Chapter 4 Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Ideas Ideas Ideas Ideas Ideas 2020-21 Page 2 Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you. 4.2 Points By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. 4.1 Introduction Chapter 4 Chapter 4 Chapter 4 Chapter 4 Chapter 4 Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Ideas Ideas Ideas Ideas Ideas 2020-21 MATHEMATICS 70 A point determines a location. These are some models for a point : If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A,B,C. These points will be read as point A, point B and point C. Of course, the dots have to be invisibly thin. 1. With a sharp tip of the pencil, mark four points on a paper and name them by the letters A,C,P ,H. Try to name these points in different ways. One such way could be this 2. A star in the sky also gives us an idea of a point. Identify at least five such situations in your daily life. 4.3 A Line Segment Fold a piece of paper and unfold it. Do you see a fold? This gives the idea of a line segment. It has two end points A and B. Take a thin thread. Hold its two ends and stretch it without a slack. It represents a line segment. The ends held by hands are the end points of the line segment. The tip of a compass The sharpened end of a pencil The pointed end of a needle lA lB lC 2020-21 Page 3 Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you. 4.2 Points By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. 4.1 Introduction Chapter 4 Chapter 4 Chapter 4 Chapter 4 Chapter 4 Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Ideas Ideas Ideas Ideas Ideas 2020-21 MATHEMATICS 70 A point determines a location. These are some models for a point : If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A,B,C. These points will be read as point A, point B and point C. Of course, the dots have to be invisibly thin. 1. With a sharp tip of the pencil, mark four points on a paper and name them by the letters A,C,P ,H. Try to name these points in different ways. One such way could be this 2. A star in the sky also gives us an idea of a point. Identify at least five such situations in your daily life. 4.3 A Line Segment Fold a piece of paper and unfold it. Do you see a fold? This gives the idea of a line segment. It has two end points A and B. Take a thin thread. Hold its two ends and stretch it without a slack. It represents a line segment. The ends held by hands are the end points of the line segment. The tip of a compass The sharpened end of a pencil The pointed end of a needle lA lB lC 2020-21 BASIC GEOMETRICAL IDEAS 71 The following are some models for a line segment : Try to find more examples for line segments from your surroundings. Mark any two points A and B on a sheet of paper. Try to connect A to B by all possible routes. (Fig 4.1) What is the shortest route from A to B? This shortest join of point A to B (including A and B) shown here is a line segment. It is denoted by or . The points A and B are called the end points of the segment. 1. Name the line segments in the figure 4.2. Is A, the end point of each line segment? An edge of a box A tube light A B Fig 4.2 4.4 A Line Imagine that the line segment from A to B (i.e. AB ) is extended beyond A in one direction and beyond B in the other direction without any end (see figure). You now get a model for a line. Do you think you can draw a complete picture of a line? No. (Why?) A line through two points A and B is written as AB s r uu . It extends indefinitely in both directions. So it contains a countless number of points. (Think about this). Two points are enough to fix a line. We say ‘two points determine a line’. The adjacent diagram (Fig 4.3) is that of a line PQ written as PQ s r uu . Sometimes a line is denoted by a letter like l, m. Fig 4.1 Fig 4.3 The edge of a post card 2020-21 Page 4 Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you. 4.2 Points By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. 4.1 Introduction Chapter 4 Chapter 4 Chapter 4 Chapter 4 Chapter 4 Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Ideas Ideas Ideas Ideas Ideas 2020-21 MATHEMATICS 70 A point determines a location. These are some models for a point : If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A,B,C. These points will be read as point A, point B and point C. Of course, the dots have to be invisibly thin. 1. With a sharp tip of the pencil, mark four points on a paper and name them by the letters A,C,P ,H. Try to name these points in different ways. One such way could be this 2. A star in the sky also gives us an idea of a point. Identify at least five such situations in your daily life. 4.3 A Line Segment Fold a piece of paper and unfold it. Do you see a fold? This gives the idea of a line segment. It has two end points A and B. Take a thin thread. Hold its two ends and stretch it without a slack. It represents a line segment. The ends held by hands are the end points of the line segment. The tip of a compass The sharpened end of a pencil The pointed end of a needle lA lB lC 2020-21 BASIC GEOMETRICAL IDEAS 71 The following are some models for a line segment : Try to find more examples for line segments from your surroundings. Mark any two points A and B on a sheet of paper. Try to connect A to B by all possible routes. (Fig 4.1) What is the shortest route from A to B? This shortest join of point A to B (including A and B) shown here is a line segment. It is denoted by or . The points A and B are called the end points of the segment. 1. Name the line segments in the figure 4.2. Is A, the end point of each line segment? An edge of a box A tube light A B Fig 4.2 4.4 A Line Imagine that the line segment from A to B (i.e. AB ) is extended beyond A in one direction and beyond B in the other direction without any end (see figure). You now get a model for a line. Do you think you can draw a complete picture of a line? No. (Why?) A line through two points A and B is written as AB s r uu . It extends indefinitely in both directions. So it contains a countless number of points. (Think about this). Two points are enough to fix a line. We say ‘two points determine a line’. The adjacent diagram (Fig 4.3) is that of a line PQ written as PQ s r uu . Sometimes a line is denoted by a letter like l, m. Fig 4.1 Fig 4.3 The edge of a post card 2020-21 MATHEMATICS 72 4.5 Intersecting Lines Look at the diagram (Fig 4.4). Two lines l 1 and l 2 are shown. Both the lines pass through point P. We say l 1 and l 2 intersect at P. If two lines have one common point, they are called intersecting lines. The following are some models of a pair of intersecting lines (Fig 4.5) : Try to find out some more models for a pair of intersecting lines. Take a sheet of paper. Make two folds (and crease them) to represent a pair of intersecting lines and discuss : (a) Can two lines intersect in more than one point? (b) Can more than two lines intersect in one point? 4.6 Parallel Lines Let us look at this table (Fig 4.6). The top ABCD is flat. Are you able to see some points and line segments? Are there intersecting line segments? Yes, AB and BC intersect at the point B. Which line segments intersect at A? at C? at D? Do the lines AD and CD intersect? Fig 4.4 Two adjacement edges of your notebook The letter X of the English alphabet Crossing-roads Fig 4.5 Fig 4.6 2020-21 Page 5 Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing etc. You observe and use different objects like boxes, tables, books, the tiffin box you carry to your school for lunch, the ball with which you play and so on. All such objects have different shapes. The ruler which you use, the pencil with which you write are straight. The pictures of a bangle, the one rupee coin or a ball appear round. Here, you will learn some interesting facts that will help you know more about the shapes around you. 4.2 Points By a sharp tip of the pencil, mark a dot on the paper. Sharper the tip, thinner will be the dot. This almost invisible tiny dot will give you an idea of a point. 4.1 Introduction Chapter 4 Chapter 4 Chapter 4 Chapter 4 Chapter 4 Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Basic Geometrical Ideas Ideas Ideas Ideas Ideas 2020-21 MATHEMATICS 70 A point determines a location. These are some models for a point : If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A,B,C. These points will be read as point A, point B and point C. Of course, the dots have to be invisibly thin. 1. With a sharp tip of the pencil, mark four points on a paper and name them by the letters A,C,P ,H. Try to name these points in different ways. One such way could be this 2. A star in the sky also gives us an idea of a point. Identify at least five such situations in your daily life. 4.3 A Line Segment Fold a piece of paper and unfold it. Do you see a fold? This gives the idea of a line segment. It has two end points A and B. Take a thin thread. Hold its two ends and stretch it without a slack. It represents a line segment. The ends held by hands are the end points of the line segment. The tip of a compass The sharpened end of a pencil The pointed end of a needle lA lB lC 2020-21 BASIC GEOMETRICAL IDEAS 71 The following are some models for a line segment : Try to find more examples for line segments from your surroundings. Mark any two points A and B on a sheet of paper. Try to connect A to B by all possible routes. (Fig 4.1) What is the shortest route from A to B? This shortest join of point A to B (including A and B) shown here is a line segment. It is denoted by or . The points A and B are called the end points of the segment. 1. Name the line segments in the figure 4.2. Is A, the end point of each line segment? An edge of a box A tube light A B Fig 4.2 4.4 A Line Imagine that the line segment from A to B (i.e. AB ) is extended beyond A in one direction and beyond B in the other direction without any end (see figure). You now get a model for a line. Do you think you can draw a complete picture of a line? No. (Why?) A line through two points A and B is written as AB s r uu . It extends indefinitely in both directions. So it contains a countless number of points. (Think about this). Two points are enough to fix a line. We say ‘two points determine a line’. The adjacent diagram (Fig 4.3) is that of a line PQ written as PQ s r uu . Sometimes a line is denoted by a letter like l, m. Fig 4.1 Fig 4.3 The edge of a post card 2020-21 MATHEMATICS 72 4.5 Intersecting Lines Look at the diagram (Fig 4.4). Two lines l 1 and l 2 are shown. Both the lines pass through point P. We say l 1 and l 2 intersect at P. If two lines have one common point, they are called intersecting lines. The following are some models of a pair of intersecting lines (Fig 4.5) : Try to find out some more models for a pair of intersecting lines. Take a sheet of paper. Make two folds (and crease them) to represent a pair of intersecting lines and discuss : (a) Can two lines intersect in more than one point? (b) Can more than two lines intersect in one point? 4.6 Parallel Lines Let us look at this table (Fig 4.6). The top ABCD is flat. Are you able to see some points and line segments? Are there intersecting line segments? Yes, AB and BC intersect at the point B. Which line segments intersect at A? at C? at D? Do the lines AD and CD intersect? Fig 4.4 Two adjacement edges of your notebook The letter X of the English alphabet Crossing-roads Fig 4.5 Fig 4.6 2020-21 BASIC GEOMETRICAL IDEAS 73 Do the lines AD s r uu and BC s r uu intersect? You find that on the table’s surface there are line segment which will not meet, however far they are extended. AD s r uu and BC s r uu form one such pair. Can you identify one more such pair of lines (which do not meet) on the top of the table? Lines like these which do not meet are said to be parallel; and are called parallel lines. Think, discuss and write Where else do you see parallel lines? Try to find ten examples. If two lines AB s r uu and CD s r uu are parallel, we write AB s r uu || CD s r uu . If two lines l 1 and l 2 are parallel, we write l 1 || l 2 . Can you identify parrallel lines in the following figures? Ray of light from a torch Sun rays Beam of light from a light house 4.7 Ray Rail lines The opposite edges of ruler (scale) The cross-bars of this window 2020-21Read More

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