Page 1 LINES AND ANGLES 93 93 93 93 93 5.1 INTRODUCTION You already know how to identify different lines, line segments and angles in a given shape. Can you identify the different line segments and angles formed in the following figures? (Fig 5.1) (i) (ii) (iii) (iv) Fig 5.1 Can you also identify whether the angles made are acute or obtuse or right? Recall that a line segment has two end points. If we extend the two end points in either direction endlessly, we get a line. Thus, we can say that a line has no end points. On the other hand, recall that a ray has one end point (namely its starting point). For example, look at the figures given below: Fig 5.2 Here, Fig 5.2 (i) shows a line segment, Fig 5.2 (ii) shows a line and Fig 5.2 (iii) is that of a ray. A line segment PQ is generally denoted by the symbol PQ , a line AB is denoted by the symbol AB and the ray OP is denoted by OP ur uu . Give some examples of line segments and rays from your daily life and discuss them with your friends. Chapter 5 Lines and Angles (iii) (i) (ii) 202021 © NCERT not to be republished Page 2 LINES AND ANGLES 93 93 93 93 93 5.1 INTRODUCTION You already know how to identify different lines, line segments and angles in a given shape. Can you identify the different line segments and angles formed in the following figures? (Fig 5.1) (i) (ii) (iii) (iv) Fig 5.1 Can you also identify whether the angles made are acute or obtuse or right? Recall that a line segment has two end points. If we extend the two end points in either direction endlessly, we get a line. Thus, we can say that a line has no end points. On the other hand, recall that a ray has one end point (namely its starting point). For example, look at the figures given below: Fig 5.2 Here, Fig 5.2 (i) shows a line segment, Fig 5.2 (ii) shows a line and Fig 5.2 (iii) is that of a ray. A line segment PQ is generally denoted by the symbol PQ , a line AB is denoted by the symbol AB and the ray OP is denoted by OP ur uu . Give some examples of line segments and rays from your daily life and discuss them with your friends. Chapter 5 Lines and Angles (iii) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 94 94 94 94 94 Again recall that an angle is formed when lines or line segments meet. In Fig 5.1, observe the corners. These corners are formed when two lines or line segments intersect at a point. For example, look at the figures given below: Fig 5.3 In Fig 5.3 (i) line segments AB and BC intersect at B to form angle ABC, and again line segments BC and AC intersect at C to form angle ACB and so on. Whereas, in Fig 5.3 (ii) lines PQ and RS intersect at O to form four angles POS, SOQ, QOR and ROP. An angle ABC is represented by the symbol ?ABC. Thus, in Fig 5.3 (i), the three angles formed are ?ABC, ?BCA and ?BAC, and in Fig 5.3 (ii), the four angles formed are ?POS, ?SOQ, ?QOR and ?POR. Y ou have already studied how to classify the angles as acute, obtuse or right angle. Note: While referring to the measure of an angle ABC, we shall write m?ABC as simply ?ABC. The context will make it clear , whether we are referring to the angle or its measure. 5.2 RELATED ANGLES 5.2.1 Complementary Angles When the sum of the measures of two angles is 90°, the angles are called complementary angles. (i) (ii) List ten figures around you and identify the acute, obtuse and right angles found in them. TRY THESE Whenever two angles are complementary, each angle is said to be the complement of the other angle. In the above diagram (Fig 5.4), the ‘30° angle’ is the complement of the ‘60° angle’ and vice versa. Are these two angles complementary? No (i) (ii) (iii) (iv) Are these two angles complementary? Yes Fig 5.4 202021 © NCERT not to be republished Page 3 LINES AND ANGLES 93 93 93 93 93 5.1 INTRODUCTION You already know how to identify different lines, line segments and angles in a given shape. Can you identify the different line segments and angles formed in the following figures? (Fig 5.1) (i) (ii) (iii) (iv) Fig 5.1 Can you also identify whether the angles made are acute or obtuse or right? Recall that a line segment has two end points. If we extend the two end points in either direction endlessly, we get a line. Thus, we can say that a line has no end points. On the other hand, recall that a ray has one end point (namely its starting point). For example, look at the figures given below: Fig 5.2 Here, Fig 5.2 (i) shows a line segment, Fig 5.2 (ii) shows a line and Fig 5.2 (iii) is that of a ray. A line segment PQ is generally denoted by the symbol PQ , a line AB is denoted by the symbol AB and the ray OP is denoted by OP ur uu . Give some examples of line segments and rays from your daily life and discuss them with your friends. Chapter 5 Lines and Angles (iii) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 94 94 94 94 94 Again recall that an angle is formed when lines or line segments meet. In Fig 5.1, observe the corners. These corners are formed when two lines or line segments intersect at a point. For example, look at the figures given below: Fig 5.3 In Fig 5.3 (i) line segments AB and BC intersect at B to form angle ABC, and again line segments BC and AC intersect at C to form angle ACB and so on. Whereas, in Fig 5.3 (ii) lines PQ and RS intersect at O to form four angles POS, SOQ, QOR and ROP. An angle ABC is represented by the symbol ?ABC. Thus, in Fig 5.3 (i), the three angles formed are ?ABC, ?BCA and ?BAC, and in Fig 5.3 (ii), the four angles formed are ?POS, ?SOQ, ?QOR and ?POR. Y ou have already studied how to classify the angles as acute, obtuse or right angle. Note: While referring to the measure of an angle ABC, we shall write m?ABC as simply ?ABC. The context will make it clear , whether we are referring to the angle or its measure. 5.2 RELATED ANGLES 5.2.1 Complementary Angles When the sum of the measures of two angles is 90°, the angles are called complementary angles. (i) (ii) List ten figures around you and identify the acute, obtuse and right angles found in them. TRY THESE Whenever two angles are complementary, each angle is said to be the complement of the other angle. In the above diagram (Fig 5.4), the ‘30° angle’ is the complement of the ‘60° angle’ and vice versa. Are these two angles complementary? No (i) (ii) (iii) (iv) Are these two angles complementary? Yes Fig 5.4 202021 © NCERT not to be republished LINES AND ANGLES 95 95 95 95 95 THINK, DISCUSS AND WRITE 1. Can two acute angles be complement to each other? 2. Can two obtuse angles be complement to each other? 3. Can two right angles be complement to each other? 1. Which pairs of following angles are complementary? (Fig 5.5) Fig 5.5 2. What is the measure of the complement of each of the following angles? (i) 45º (ii) 65º (iii) 41º (iv) 54º 3. The difference in the measures of two complementary angles is 12 o . Find the measures of the angles. 5.2.2 Supplementary Angles Let us now look at the following pairs of angles (Fig 5.6): TRY THESE (i) (ii) (iii) (iv) (i) (ii) 202021 © NCERT not to be republished Page 4 LINES AND ANGLES 93 93 93 93 93 5.1 INTRODUCTION You already know how to identify different lines, line segments and angles in a given shape. Can you identify the different line segments and angles formed in the following figures? (Fig 5.1) (i) (ii) (iii) (iv) Fig 5.1 Can you also identify whether the angles made are acute or obtuse or right? Recall that a line segment has two end points. If we extend the two end points in either direction endlessly, we get a line. Thus, we can say that a line has no end points. On the other hand, recall that a ray has one end point (namely its starting point). For example, look at the figures given below: Fig 5.2 Here, Fig 5.2 (i) shows a line segment, Fig 5.2 (ii) shows a line and Fig 5.2 (iii) is that of a ray. A line segment PQ is generally denoted by the symbol PQ , a line AB is denoted by the symbol AB and the ray OP is denoted by OP ur uu . Give some examples of line segments and rays from your daily life and discuss them with your friends. Chapter 5 Lines and Angles (iii) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 94 94 94 94 94 Again recall that an angle is formed when lines or line segments meet. In Fig 5.1, observe the corners. These corners are formed when two lines or line segments intersect at a point. For example, look at the figures given below: Fig 5.3 In Fig 5.3 (i) line segments AB and BC intersect at B to form angle ABC, and again line segments BC and AC intersect at C to form angle ACB and so on. Whereas, in Fig 5.3 (ii) lines PQ and RS intersect at O to form four angles POS, SOQ, QOR and ROP. An angle ABC is represented by the symbol ?ABC. Thus, in Fig 5.3 (i), the three angles formed are ?ABC, ?BCA and ?BAC, and in Fig 5.3 (ii), the four angles formed are ?POS, ?SOQ, ?QOR and ?POR. Y ou have already studied how to classify the angles as acute, obtuse or right angle. Note: While referring to the measure of an angle ABC, we shall write m?ABC as simply ?ABC. The context will make it clear , whether we are referring to the angle or its measure. 5.2 RELATED ANGLES 5.2.1 Complementary Angles When the sum of the measures of two angles is 90°, the angles are called complementary angles. (i) (ii) List ten figures around you and identify the acute, obtuse and right angles found in them. TRY THESE Whenever two angles are complementary, each angle is said to be the complement of the other angle. In the above diagram (Fig 5.4), the ‘30° angle’ is the complement of the ‘60° angle’ and vice versa. Are these two angles complementary? No (i) (ii) (iii) (iv) Are these two angles complementary? Yes Fig 5.4 202021 © NCERT not to be republished LINES AND ANGLES 95 95 95 95 95 THINK, DISCUSS AND WRITE 1. Can two acute angles be complement to each other? 2. Can two obtuse angles be complement to each other? 3. Can two right angles be complement to each other? 1. Which pairs of following angles are complementary? (Fig 5.5) Fig 5.5 2. What is the measure of the complement of each of the following angles? (i) 45º (ii) 65º (iii) 41º (iv) 54º 3. The difference in the measures of two complementary angles is 12 o . Find the measures of the angles. 5.2.2 Supplementary Angles Let us now look at the following pairs of angles (Fig 5.6): TRY THESE (i) (ii) (iii) (iv) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 96 96 96 96 96 Fig 5.6 Do you notice that the sum of the measures of the angles in each of the above pairs (Fig 5.6) comes out to be 180º? Such pairs of angles are called supplementary angles. When two angles are supplementary , each angle is said to be the supplement of the other. THINK, DISCUSS AND WRITE 1. Can two obtuse angles be supplementary? 2. Can two acute angles be supplementary? 3. Can two right angles be supplementary? 1. Find the pairs of supplementary angles in Fig 5.7: Fig 5.7 (iii) (iv) TRY THESE (iii) (iv) (i) (ii) 202021 © NCERT not to be republished Page 5 LINES AND ANGLES 93 93 93 93 93 5.1 INTRODUCTION You already know how to identify different lines, line segments and angles in a given shape. Can you identify the different line segments and angles formed in the following figures? (Fig 5.1) (i) (ii) (iii) (iv) Fig 5.1 Can you also identify whether the angles made are acute or obtuse or right? Recall that a line segment has two end points. If we extend the two end points in either direction endlessly, we get a line. Thus, we can say that a line has no end points. On the other hand, recall that a ray has one end point (namely its starting point). For example, look at the figures given below: Fig 5.2 Here, Fig 5.2 (i) shows a line segment, Fig 5.2 (ii) shows a line and Fig 5.2 (iii) is that of a ray. A line segment PQ is generally denoted by the symbol PQ , a line AB is denoted by the symbol AB and the ray OP is denoted by OP ur uu . Give some examples of line segments and rays from your daily life and discuss them with your friends. Chapter 5 Lines and Angles (iii) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 94 94 94 94 94 Again recall that an angle is formed when lines or line segments meet. In Fig 5.1, observe the corners. These corners are formed when two lines or line segments intersect at a point. For example, look at the figures given below: Fig 5.3 In Fig 5.3 (i) line segments AB and BC intersect at B to form angle ABC, and again line segments BC and AC intersect at C to form angle ACB and so on. Whereas, in Fig 5.3 (ii) lines PQ and RS intersect at O to form four angles POS, SOQ, QOR and ROP. An angle ABC is represented by the symbol ?ABC. Thus, in Fig 5.3 (i), the three angles formed are ?ABC, ?BCA and ?BAC, and in Fig 5.3 (ii), the four angles formed are ?POS, ?SOQ, ?QOR and ?POR. Y ou have already studied how to classify the angles as acute, obtuse or right angle. Note: While referring to the measure of an angle ABC, we shall write m?ABC as simply ?ABC. The context will make it clear , whether we are referring to the angle or its measure. 5.2 RELATED ANGLES 5.2.1 Complementary Angles When the sum of the measures of two angles is 90°, the angles are called complementary angles. (i) (ii) List ten figures around you and identify the acute, obtuse and right angles found in them. TRY THESE Whenever two angles are complementary, each angle is said to be the complement of the other angle. In the above diagram (Fig 5.4), the ‘30° angle’ is the complement of the ‘60° angle’ and vice versa. Are these two angles complementary? No (i) (ii) (iii) (iv) Are these two angles complementary? Yes Fig 5.4 202021 © NCERT not to be republished LINES AND ANGLES 95 95 95 95 95 THINK, DISCUSS AND WRITE 1. Can two acute angles be complement to each other? 2. Can two obtuse angles be complement to each other? 3. Can two right angles be complement to each other? 1. Which pairs of following angles are complementary? (Fig 5.5) Fig 5.5 2. What is the measure of the complement of each of the following angles? (i) 45º (ii) 65º (iii) 41º (iv) 54º 3. The difference in the measures of two complementary angles is 12 o . Find the measures of the angles. 5.2.2 Supplementary Angles Let us now look at the following pairs of angles (Fig 5.6): TRY THESE (i) (ii) (iii) (iv) (i) (ii) 202021 © NCERT not to be republished MATHEMATICS 96 96 96 96 96 Fig 5.6 Do you notice that the sum of the measures of the angles in each of the above pairs (Fig 5.6) comes out to be 180º? Such pairs of angles are called supplementary angles. When two angles are supplementary , each angle is said to be the supplement of the other. THINK, DISCUSS AND WRITE 1. Can two obtuse angles be supplementary? 2. Can two acute angles be supplementary? 3. Can two right angles be supplementary? 1. Find the pairs of supplementary angles in Fig 5.7: Fig 5.7 (iii) (iv) TRY THESE (iii) (iv) (i) (ii) 202021 © NCERT not to be republished LINES AND ANGLES 97 97 97 97 97 2. What will be the measure of the supplement of each one of the following angles? (i) 100º (ii) 90º (iii) 55º (iv) 125º 3. Among two supplementary angles the measure of the larger angle is 44 o more than the measure of the smaller. Find their measures. 5.2.3. Adjacent Angles Look at the following figures: Fig 5.8 At both the vertices A and B, we find, a pair of angles are placed next to each other. These angles are such that: (i) they have a common vertex; (ii) they have a common arm; and (iii) the noncommon arms are on either side of the common arm. Such pairs of angles are called adjacent angles. Adjacent angles have a common vertex and a common arm but no common interior points. 1. Are the angles marked 1 and 2 adjacent? (Fig 5.9). If they are not adjacent, say, ‘why’. A B When you open a book it looks like the above figure. In A and B, we find a pair of angles, placed next to each other. Look at this steering wheel of a car. At the centre of the wheel you find three angles being formed, lying next to one another. TRY THESE (i) (ii) (iii) 202021 © NCERT not to be republishedRead More
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
165 videos252 docs45 tests
