202110181-APEX-STUDENT-WORKBOOK-MATHEMATICS-G06-PART1

6. [AS4] For a morning walk, three persons step off together.Their steps measure 80 cm, 85 cm and 90 cm respectively. The minimum distance each should walk so that all can cover the same distance in complete steps is . (A) 12470 cm (B) 12240 cm (C)12860 cm (D)None of these 7. [AS4] Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. The number of times they toll together in 30 minutes is . (A) 4 (B) 10 (C) 15 (D) 16 8. [AS4] A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. The time after which they will meet again at the starting point is . (A) 26 minutes and 18 seconds (B) 42 minutes and 36 seconds (C)45 minutes (D)46 minutes and 12 seconds Short Answer Type Questions 9(i) [AS1] The HCF and LCM of two numbers are 13 and 1989 respectively. If one of the numbers is 117, find the other. (ii) [AS1] The LCM of two numbers is 1320. Their HCF is 12. If one of the numbers is 132, find the other. 10(i) [AS1] The product of two numbers is 8400. Their HCF is 20. Find the LCM of these two numbers. (ii) [AS1] The LCM and HCF of two numbers are 4125 and 25 respectively. One number is 375. By how much is the second number less than the first? 11(i) [AS1] The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, find the other. (ii) [AS1] The LCM of two numbers is 360 and their HCF is 72. One of the numbers is 1 1 times 4 the other number. Find the two numbers. 12 [AS2] Can two numbers have 14 as their H.C.F and 204 as their L.C.M ? Give reasons in support of your answer. EXERCISE 3.6. RELATIONSHIP BETWEEN LCM AND HCF 48

EXERCISE 3.7 DIVISIBILITY RULES FOR 4, 8 AND 11 3.7.1 Key Concepts i. A number is divisible by 4, if the number formed by its last two digits (i.e., tens and ones) is divisible by 4. ii. A number with 4 or more digits is divisible by 8, if the number formed by its last three digits is divisible by 8. iii. A given number is divisible by 11, if the difference between the sum of the digits at odd places and the sum of the digits at even places (from the right) is either 0 or divisible by 11. 3.7.2 Additional Questions Objective Questions . 1. [AS3] The number divisible by 4 is (B) 3462 (D) 8542 (A) 3472 (C) 3570 . 2. [AS3] The number divisible by 8 is (A) 8542 (B) 3570 (C) 3472 (D) 3462 3. [AS3] The number divisible by 4 is divisible by 8. (A) Always (B) Sometimes (C) Never (D)None of these 4. [AS3] A number divisible by 8 is divisible by 4. (A) Always (B) Sometimes (C) Never (D)None of these EXERCISE 3.7. DIVISIBILITY RULES FOR 4, 8 AND 11 49

5. [AS1] The number 34856p72 is divisible by 11. Then 'p' is . (A) 0 (B) 1 (C) 2 (D) 3 Very Short Answer Type Questions 6 [AS3] Choose the correct answer. (i) The number 4312 is divisible by . (A) 6 (B) 5 (C) 4 . (D) 3 (ii) The number which is divisible by 4 is (B) 1326 (D) 6782 (A) 3428 (C) 4330 (B) 8475671 (D) 9000004 (iii) The number which is divisible by 4 is . (A) 948762 (C) 80004010 (iv) The number 567428 is divisible by . (A) 4 (B) 5 (C) 7 (D) 9 (v) The number which is not divisible by 4 is . (A) 2304 (B) 5600 (C) 8734 (D) 900132 Short Answer Type Questions 7(i) [AS2] Verify whether the following numbers are divisible by 4 or not. a) 576432 b) 897300 (ii) [AS2] Verify whether the number 3400561 is divisible by 4 or not and also find the least number that should be added to the given number so that the result is divisible by 4. 8(i) [AS2] Verify whether the following numbers are divisible by 8 or not. a) 76500164 b) 9005432 EXERCISE 3.7. DIVISIBILITY RULES FOR 4, 8 AND 11 50

(ii) [AS2] Check whether the numbers are divisible by 8 or not and also verify it by actual division. a) 654321 b) 8765408 9(i) [AS2] Check whether the number 78654323 is divisible by 11 or not. (ii) [AS2] Check whether the number 348936542 is divisible by 11 or not. Also verify this by actual division. 10(i) [AS2] Check whether the number 846320 is divisible by 4 and 8 or not. (ii) [AS2] Check whether the number 1289460 is divisible by 4 and 8 or not. Also verify by actual division. EXERCISE 3.7. DIVISIBILITY RULES FOR 4, 8 AND 11 51

CHAPTER 4 BASIC GEOMETRICAL IDEAS EXERCISE 4.1 POINT, LINE SEGMENT, LINE AND RAY 4.1.1 Key Concepts i. A point determines a location. It is usually denoted by a capital letter. ‘P’ is a point on the line ‘l’. ii. A line segment is formed by joining two points. It has a fixed length. iii. A line is obtained when a line segment extends on both sides indefinitely. iv. The line ‘n’ is obtained when PQ is extended on both sides indefinitely. v. A ray is a portion of a line starting at a point and goes in one direction endlessly. OA is a ray. It starts at ‘O’ and passes through the point A. EXERCISE 4.1. POINT, LINE SEGMENT, LINE AND RAY 52

4.1.2 Additional Questions . Objective Questions 1. [AS5] A point among the following is (A) (B) (C) (D) . 2. [AS5] A line segment among the following is (A) (B) (C) (D) 3. [AS3] A ray has _______ end point(s). (A) 0 (B) 1 (C) 2 (D) No 4. [AS3] A line extends in directions. (A) No (B) One (C) Both (D) All EXERCISE 4.1. POINT, LINE SEGMENT, LINE AND RAY 53

5. [AS5] The points that belong to the line ’l ’ in the given figure are . (A) S, Q (B) R, P (C)S, P (D)R, S Very Short Answer Type Questions 6 [AS3] Fill in the blanks. (i) A has one end point. (ii) A line has end points. (iii) A line has no definite length because it has . end points. (iv) A line segment has length because it has . [AS3] Answer the following questions in one sentence. (v) How many end points does a line segment have? 7 [AS3] Fill in the blanks. (i) A line segment when extended on both the sides gives (ii) In a ray , the point ’O’ is called point. (iii) is a . . . (iv) The number of lines that can be drawn passing through two points is (v) A and B are points on a Short Answer Type Questions 8 [AS4] Give three examples of line segments from your surroundings. EXERCISE 4.1. POINT, LINE SEGMENT, LINE AND RAY 54

9(i) [AS5] Name any four points from the following figure. (ii) [AS5] Name any six line segments from the following figure. 10(i) [AS5] Mark two points P and Q and draw a line passing through P and Q. Name it. How many such lines can you draw? (ii) [AS5] Mark any three points P, Q and R. Draw a line passing through two points P and Q. What can you say about the third point R? 11(i) [AS5] Draw a line, mark two points on it and name the line. (ii) [AS5] Mark two points A and B. Draw a line through the points A and B. Mark a point P on it other than A and B. Draw three lines passing through the point P. EXERCISE 4.1. POINT, LINE SEGMENT, LINE AND RAY 55

EXERCISE 4.2 CURVE AND POLYGONS 4.2.1 Key Concepts i. Any figure drawn without lifting a pencil may be called a curve. In this sense, a line is also a curve. ii. A simple curve is the one that does not cross itself. iii. A closed figure bounded with line segments is called a polygon. iv. Curves are of two types – open and closed. EXERCISE 4.2. CURVE AND POLYGONS 56

4.2.2 Additional Questions . Objective Questions 1. [AS5] Among the following, a simple closed curve is (A) (B) (C) (D)None of these 2. [AS5] is an example of curve. (A) A simple closed (B) An open (C)A concave (D)None of these EXERCISE 4.2. CURVE AND POLYGONS 57

3. [AS5] A point in the interior of the given simple closed figure is . (A) P (B) Q (C) R (D)None of these 4. [AS5] A point that belongs to the given figure is . (A) P (B) Q (C) R (D) S 5. [AS5] A point in the exterior of the given simple closed figure is . (A) P (B) Q . (D) S (C) R Very Short Answer Type Questions curve. 6 [AS3] Fill in the blanks. (i) A straight line is also a (ii) If a curve does not cross itself, then it is a EXERCISE 4.2. CURVE AND POLYGONS 58

[AS3] Answer the following questions in one sentence. (iii) Name the closed curves from the following. (iv) Mark simple curves among the following. (v) Identify which are simple curves and which are not. 7 [AS3] Fill in the blanks. curve. . (i) is an example of (ii) is an example of a (iii) A circle is an example for a curve. (iv) A closed figure that does not intersect itself is called a figure. EXERCISE 4.2. CURVE AND POLYGONS 59

[AS3] Answer the following questions in one sentence. (v) Mark the one which is not a closed curve. 8 [AS5] Choose the correct answer. . (i) A point in the interior of the figure is (A) P (B) Q (C) R (D) S (ii) The point that lies in the exterior of the triangle ABC is . (A) P (B) Q (C) R (D) None of these (iii) The point that lies on the boundary of the rectangle ABCD is . (A) R (B) Q (C) P (D) None of these EXERCISE 4.2. CURVE AND POLYGONS 60

(iv) A point that belongs to the given circle is . (A) O (B) S (C) Q (D) P (v) The point that belongs to the interior of the given closed figure is . (A) P (B) Q (C) R (D) S 9 [AS5] Answer the following questions in one sentence. (i) Draw a simple closed figure of three sides. (ii) Draw a simple closed figure of six sides. (iii) Draw a simple closed figure of eight sides. (iv) Draw a simple closed figure of five sides. EXERCISE 4.2. CURVE AND POLYGONS 61

EXERCISE 4.3 ANGLE 4.3.1 Key Concepts i. An angle is made up of two rays starting from a common end point. The common end point is called the vertex and the two rays are the arms of the angle. In the given figure, ‘O’ is the vertex. −−→ and −−→ are two arms or sides of the angle AOB or BOA. OA OB Symbol: ∠ AOB or ∠ BOA; A O∧ B or ∧ A BO ii. Every angle divides the plane as interior, exterior and boundary of the angle. 4.3.2 Additional Questions Objective Questions 1. [AS5] The vertex of the angle is . (A) A (B) B (C) O (D)None of these EXERCISE 4.3. ANGLE 62

2. [AS5] The initial ray of the given angle is . (AA) −−→ (B) −−→ O OB (C) ∠AOB (D)None of these 3. [AS5] The point in the interior of the angle in the figure is . (A) V (B) R (C) T (D) Q 4. [AS5] The point in the exterior of the angle ∠LMN is . (A) P (B) Q (C) R (D) S EXERCISE 4.3. ANGLE 63

5. [AS5] The point that belongs to ∠ABC is . (A) P (B) Q (D) S (C) R Very Short Answer Type Questions 6 [AS5] Fill in the blanks. (i) An angle is represented as ∠O . (ii) The vertex of the angle given is A. . (iii) The arms of the angle are . (iv) The angle in the figure is represented as or . (v) In general, while representing an angle by using three letters, the middle letter is the vertex of the angle. Short Answer Type Questions 7 [AS4] Give two examples of a right angle from your surroundings. EXERCISE 4.3. ANGLE 64

8(i) [AS5] Which of the following points are in the interior of ∠ABC? (ii) [AS5] a) Which of the points are in the exterior of the ∠QPR? b) Mark three points in the interior of ∠ABC and name them. c) Mark three points in the exterior of ∠PQR and name them. 9(i) [AS5] Draw a triangle PQR, mark the angles in the triangle and name them. (ii) [AS5] Draw a quadrilateral ABCD, draw its diagonals and write the names of the some angles formed in the quadrilateral ABCD. EXERCISE 4.3. ANGLE 65

EXERCISE 4.4 TRIANGLE AND QUADRILATERAL 4.4.1 Key Concepts i. A triangle is a simple closed figure bounded by three line segments. ii. A triangle has three vertices, three sides and three angles. A, B and C are the vertices of triangle ABC. AB, BC, CA are the sides of triangle ABC. ∠BAC, ∠ABC, ∠ACB are the three angles of triangle ABC. iii. A triangle with its boundary and interior is called the triangular region. iv. A quadrilateral is a simple closed figure bounded by four line segments. It has four vertices, four sides, four angles and two diagonals. AB, BC, CD, DA are the four sides of quadrilateral ABCD. A, B, C, D are its vertices. ∠DAB, ∠ABC, ∠BCD, ∠CDA are its angles and AC and BD are its two diagonals. EXERCISE 4.4. TRIANGLE AND QUADRILATERAL 66

4.4.2 Additional Questions Objective Questions 1. [AS3] The number of line segments in a triangle is . . (A) 1 (B) 2 . (C) 3 (D) 4 2. [AS3] The number of vertices in a quadrilateral is (A) 1 (B) 2 (C) 3 (D) 4 3. [AS3] The number of diagonals in a quadrilateral is (A) 1 (B) 2 (C) 3 (D) 4 4. [AS5] A point in the interior of triangle ABC is . (A) P (B) Q (C) R (D) S 5. [AS5] A point in the exterior of quadrilateral ABCD is . (A) P (B) Q (C) R (D) S EXERCISE 4.4. TRIANGLE AND QUADRILATERAL 67

Very Short Answer Type Questions 6 [AS5] Fill in the blanks. (i) The simple closed figure formed by three line segments is called . . (ii) To make a triangle, the number of sides required is . (iii) Number of vertices formed in making a triangle is . (iv) The side opposite to ∠B in ABC is . (v) The angle opposite to PQ in PQR is 7 [AS5] Fill in the blanks. . (i) is . (ii) . is (iii) . is (iv) If a simple closed figure is formed by 5 sides then it is . (v) A simple closed figure with four vertices is known as EXERCISE 4.4. TRIANGLE AND QUADRILATERAL 68

8 [AS5] Fill in the blanks. . (i) In quadrilateral PQRS, the vertices opposite to P and S are (ii) The adjacent side(s) to QR in quadrilateral PQRS is/ are . (iii) The opposite angle of Q in the quadrilateral PQRS is . EXERCISE 4.4. TRIANGLE AND QUADRILATERAL 69

(iv) The angle adjacent to ∠B in the quadrilateral ABCD is . [AS5] Answer the following questions in one sentence. (v) How many pairs of opposite sides are there in a quadrilateral? Short Answer Type Questions 9(i) [AS5] Mark any four points A, B, C and D such that no three points lie on the same straight line. Can you complete the quadrilateral with these four points? (ii) [AS5] Mark any four points on a plane surface and join them in order to form a quadrilateral. Long Answer Type Questions 10 [AS5] Draw a quadrilateral PQRS and mark four points each in the interior, in the exterior and on the boundary of the quadrilateral PQRS. EXERCISE 4.4. TRIANGLE AND QUADRILATERAL 70

EXERCISE 4.5 CIRCLE 4.5.1 Key Concepts i. A circle is a simple closed curve, in which each point on the boundary is at an equal distance from the centre. This fixed distance is called its radius. ii. The total length of the curved edge of the circle is called its circumference and a part of the circumference is called an arc. iii. A chord of a circle is a line segment joining any two points on the circle. iv. A diameter of a circle is a chord that passes through its centre. v. A circle with its boundary and interior together is a circular region. vi. The region in a circle bounded by two radii and an arc is called the sector. vii. The region in a circle bounded by a chord and an arc is called the segment of the circle. viii. A semi–circle is half of the circle. Each diameter divides a circle into two semi–circles. 4.5.2 Additional Questions Objective Questions 1. [AS3] A set of points which are equidistant from a fixed point is called a . (A) Square (B) Circle (C) Triangle (D)None of these 2. [AS3] A part of the circumference of a circle is called (A) An arc (B) A chord (C)A segment (D)None of these 3. [AS5] A point in the interior of the given circle is . (A) End point of a diameter (B) End points of a chord (C)Centre of the circle (D)None of these EXERCISE 4.5. CIRCLE 71

4. [AS5] The point that belongs to the circle is . (A) P (B) Q (C) R (D) S 5. [AS5] The point in the exterior of the circle is . (A) P (B) Q (C) R (D) S Very Short Answer Type Questions 6 [AS3] Fill in the blanks. its radius. (i) The diameter of a circle is (ii) The total length of the circle is called its . (iii) A circle with its boundary and interior together is called a region. (iv) The region of a circle bounded by a chord and the arc is called a of the circle. (v) Each diameter divides the circle into semicircles. 7 [AS5] Fill in the blanks. (i) The point which is equidistant from all the points on a circle is called the of the circle. EXERCISE 4.5. CIRCLE 72

(ii) In the given figure, AO is of the circle. (iii) The boundary of a circle is called the of the circle. (iv) The number of diameters that can be drawn in a circle is . (v) The region enclosed by and is called the sector of the circle. Short Answer Type Questions 8(i) [AS3] Define a) centre of a circle. b) an arc of a circle. c) Chord of the circle (ii) [AS3] Define a) Radius b) Diameter 9(i) [AS3] Define a) minor sector b) major sector of circle and represent both in a circle. (ii) [AS3] Define (a) minor segment (b) major segment (c) semi–circular region and represent them in a circle. Long Answer Type Questions 10 [AS5] Observe the following figure and fill in the blanks with the appropriate name: a) AB = . b) PQ = . EXERCISE 4.5. CIRCLE 73

c) Radius = times PQ. d) The region between arc ACB and chord AB is . e) The part of the circle, ADB is called . 11 [AS5] In the given figure, mark the following: i) Radius AO ii) Diameter PQ iii) Chord MN iv) Sector AOC v) Segment AB 12 [AS5] Draw a circle. Mark its centre, two radii and shade the sectors with different lines and name them. Also name the minor and major arcs. 13 [AS5] a) AB is called the of the circle. b) The longest chord in a circle is called the . EXERCISE 4.5. CIRCLE 74

c) The diameter divides the circle into two . d) In the given figure, AOB is called a . e) The major segment in the given figure is . 14 [AS5] Draw a circle with centre ‘O’. Draw a chord AB, mark minor segment and major segment with different regions. EXERCISE 4.5. CIRCLE 75

CHAPTER 5 MEASURES OF LINES AND ANGLES EXERCISE 5.1 MEASURE OF A LINE SEGMENT 5.1.1 Key Concepts i. A line segment is a part of a line with two end points. ii. We compare two line segments by simple observation, by tracing the line segments and by using instruments. iii. The instruments used to compare and draw line segments are ruler and divider. A unit of measuring length of line segments is 1 centimetre (1 cm); 1 cm = 10 mm. 5.1.2 Additional Questions Objective Questions 1. [AS3] The true statement from the given line segments is . (A) AB > PQ (B) AB < PQ (C)AB = PQ (D)None of these 2. [AS3] In general, small lengths are measured in . (A) cm (B) m (C) km (D)None of these EXERCISE 5.1. MEASURE OF A LINE SEGMENT 76

3. [AS5] The number of line segments in the figure is . (A) 3 (B) 4 (C) 5 (D) 6 4. [AS5] The mid point of the line segment AB is . (A) P (B) Q (C) R (D) S 5. [AS5] The number of mid points a line segment has is . (A) 0 (B) 1 (C) 2 (D) 4 6. [AS1] If A, B and C are three points on a line such that AB = 5 cm and AC = 8 cm, then BC = . (A) 2 cm (B) 3 cm (C)4 cm (D)6 cm 7. [AS5] If A, B and C are collinear, AB = 2.4 cm and BC = 4.8 cm then AC = . (A) 7.8 cm (B) 7.4 cm (C)7.2 cm (D)9.2 cm Very Short Answer Type Questions and 8 [AS3] Fill in the blanks. (i) Instruments used usually to compare and draw line segments are . (ii) Unit of measuring length, 1 centimetre = mm. EXERCISE 5.1. MEASURE OF A LINE SEGMENT 77

9 [AS3] Fill in the blanks. (i) To measure the length of AB given below the zero mark of the ruler should be placed at . (ii) If you place the 2 cm mark of the ruler at A and the mark against B would be 7.5 cm, then the length of AB is . (iii) To measure the length of a segment AB using divider, the metal end points are to be placed at and . Short Answer Type Questions 10 [AS4] Give any three examples of line segments observed in your class room and measure them. 11 [AS3] Why is it better to use a divider than a ruler, while comparing two line segments? 12(i) [AS5] Identify and name the line segments in the diagram. (ii) [AS5] Identify and name the line segments in the following diagrams. 13(i) [AS5] Draw two line segments on a paper, name them and compare them using a trace paper. (ii) [AS5] Draw three line segments AB , LM and PQ . Compare them by using trace paper. 14(i) [AS5] Draw a line segment, measure it and mark the mid point of the line segment. (ii) [AS5] Draw a triangle PQR, measure the lengths of its sides. Mark the mid points of the sides and name them as X, Y and Z respectively. EXERCISE 5.1. MEASURE OF A LINE SEGMENT 78

EXERCISE 5.2 MEASURE OF AN ANGLE 5.2.1 Key Concepts i. An angle is the union of two different rays with a common initial point. ii. A protractor is a semi–circular curved model with 180° equal divisions used to measure and construct angles. iii. The unit of measuring an angle is a degree (1°). It is a part of one rotation. iv. Angles where the ray moves in the opposite direction of the hands of a clock are called anticlockwise angles. −−→ −−→ v. OA is the initial ray. It is moved in the opposite direction of the hands of a clock and reaches OB , making an angle AOB. vi. Angles where the ray moves in the direction of the hands of a clock are called clockwise angles. −−→ is the initial ray. It is moved in the direction of the hands of a clock and reaches O−−→B, vii. OA making an angle AOB. viii. Kinds of angles: a. Acute angle EXERCISE 5.2. MEASURE OF AN ANGLE 79

b. Right angle c. Straight angle d. Obtuse angle e. Reflex angle 5.2.2 Additional Questions Objective Questions 1. [AS5] (A) An acute is angle. (C)A reflex (B) An obtuse (D)A right EXERCISE 5.2. MEASURE OF AN ANGLE 80

2. [AS5] The obtuse angle among the following is . (A) (B) (C) (D) 3. [AS3] If the terminal ray rotates in anticlockwise direction then we get a . 81 (A) Zero angle (B) Positive angle (C)Negative angle (D)None of these 4. [AS3] The smallest of these four angles is . (A) A straight angle (B) An obtuse angle (C)A right angle (D)An acute angle 5. [AS3] A reflex angle measures degrees. (A) 190 (B) 280 (C) 140 (D) None of these EXERCISE 5.2. MEASURE OF AN ANGLE

6. [AS4] If a bicycle wheel has 36 spokes, then the angle between a pair of adjacent spokes is . (B) 15◦ (A) 10 ◦ (C) 20◦ (D) 12◦ 7. [AS4] A bicycle wheel makes four and a half turns. The number of right angles through which it turns is . (A) 18 (B) 12 (C) 16 (D) 24 8. [AS4] Shikha is rowing a boat due north – east. The direction in which she will be rowing if she turns it through a straight angle is . (A) North – East (C) West (B) South – West (D) East Very Short Answer Type Questions . 9 [AS5] Choose the correct answer. (i) The type of angle between the hands in the clock given is (A) An acute angle (B)An obtuse angle (C)A right angle (D)A reflex angle EXERCISE 5.2. MEASURE OF AN ANGLE 82

(ii) The type of the angle between the pages of this book is . (A) An acute angle (B) An obtuse angle (C)A right angle (D)A reflex angle (iii) The angle between the top and a leg of this table is . (A) An acute angle (B) An obtuse angle (C)A right angle (D)A reflex angle (iv) The angle between the spokes of the wheel of a cycle is . (A) An acute angle (B) An obtuse angle (C) A right angle (D) A straight angle 10 [AS5] Fill in the blanks. (i) The angle ’x’ in the given figure is an acute angle . 83 EXERCISE 5.2. MEASURE OF AN ANGLE

(ii) The angle ’x’ in the given figure is an obtuse angle . (iii) The angle ’x’ in the given figure is a right angle . (iv) The angle ’x’ in the given figure is a straight angle . (v) The angle ’x’ in the given figure is a reflex angle . Short Answer Type Questions 11(i) [AS1] Find 2 of a right angle. 3 (ii) [AS1] Find 2 of a complete angle. 9 12 [AS3] Define a reflex angle. 13(i) [AS5] Use the angle apparatus and identify whether the angles given are acute, right or obtuse angle. (ii) [AS5] Using the angle apparatus, identify the angles of the given figure and classify them. EXERCISE 5.2. MEASURE OF AN ANGLE 84

14(i) [AS5] Draw any two angles. Compare them and identify which one is greater. (ii) [AS5] Draw any three angles, measure them and write the angles in ascending order of their magnitude. Long Answer Type Questions 15 [AS5] Draw and represent the angles given. (i) Acute angle (ii) Right angle (iii) Straight angle (iv) Obtuse angle (v) Reflex angle 16 [AS5] Name the angles represented by the following figures: EXERCISE 5.2. MEASURE OF AN ANGLE 85

EXERCISE 5.3 INTERSECTING LINES, PERPENDICULAR LINES AND PARALLEL LINES 5.3.1 Key Concepts LINES: i. Parallel lines ii. Perpendicular lines iii. Intersecting lines 5.3.2 Additional Questions . Objective Questions 1. [AS3] The number of points of intersection of two straight lines is (A) 0 (B) 1 (C) 2 (D)None of these 2. [AS3] The distance between lines at any point is the same. (A) Parallel (B) Perpendicular (C) Intersecting (D)None of these EXERCISE 5.3. INTERSECTING LINES, PERPENDICULAR LINES AND PAR. . . 86

3. [AS3] If two lines are perpendicular to the same line the two lines are_______ to each other. (A) Intersecting (B) Perpendicular (C) Parallel (D)None of these 4. [AS5] A pair of parallel lines in the figure given is . (A) (AB, CD) (B) (EF, DC) (C)(AB, EF) (D)(AB, ED) 5. [AS3] The angle between two perpendicular lines is . (A) 0◦ (B) 90◦ (C) 180◦ (D) 360◦ Very Short Answer Type Questions 6 [AS5] Answer the following questions in one sentence. (i) Draw two lines such that they have no point in common. (ii) Draw two lines l and m such that they have one point in common. (iii) Draw two lines having more points in common. What do you call such lines? 7 [AS5] Fill in the blanks. . (i) The diagonals of a square are (ii) The opposite sides of a rectangle are . (iii) The two adjacent sides of a rectangle are . EXERCISE 5.3. INTERSECTING LINES, PERPENDICULAR LINES AND PAR. . . 87

(iv) The two diameters of the circle given are . (v) Sides AB and DA of the square ABCD given are . Short Answer Type Questions 8(i) [AS4] Write any two examples of parallel lines in your class room. (ii) [AS4] Give any three examples of parallel lines from your daily life. 9(i) [AS4] Give two examples of perpendicular lines in your classroom. (ii) [AS4] Give three examples for perpendicular lines in your daily life. 10(i) [AS5] Draw two lines such that they are perpendicular to each other. (ii) [AS5] Draw three different lines l , m and n such that l ⊥ m and m ⊥ n. Is l ⊥n? 11 (i) [AS5] Identify the lines that are parallel in the following figures. a) EXERCISE 5.3. INTERSECTING LINES, PERPENDICULAR LINES AND PAR. . . 88

b) (ii) [AS5]@Identify the lines which are perpendicular to each other in the following figures. a) b) EXERCISE 5.3. INTERSECTING LINES, PERPENDICULAR LINES AND PAR. . . 89

Long Answer Type Questions 12 [AS5] Match the lines represented in the figures given in Group A with the types of lines given in Group B. Group A Group B 1) ( ) a) Intersecting lines 2) ( ) b) Parallel lines 3) ( ) c) Perpendicular lines 4) ( ) d) BC AB 5) ( ) e) AB DC f) PQ QR g) PQ S R EXERCISE 5.3. INTERSECTING LINES, PERPENDICULAR LINES AND PAR. . . 90

CHAPTER 7 FRACTIONS AND DECIMALS EXERCISE 7.1 TYPES OF FRACTIONS 7.1.1 Key Concepts i. Fraction: A fraction means a part of a group or of a whole. For example,35 is a fraction. Here, 3 is called the numerator and 5 is called the denominator. ii. Kinds of fractions: Proper fraction: A fraction is said to be a proper fraction if its numerator is less than its denominator. Ex: 2 , 5 etc. 7 9 Improper fraction: A fraction is said to be an improper fraction if its numerator is greater than or equal to its denominator. Ex: 7 , 9 , 6 etc. 2 5 6 Mixed fraction: An improper fraction can be written as a combination of a whole and a part. Such a fraction is called a mixed fraction. Ex: 4 3 , 2 1 , 7 5 etc. 5 3 6 23 3 3 1 1 5 5 5 = 4 5 = 4 + 5 ; 2 3 = 2 + 3 ; 7 6 = 7 + 6 Mixed fraction = (whole) + (part) . 7.1.2 Additional Questions Objective Questions 1. [AS3] A number representing a part of is called a fraction. (A) A number (B) An integer (C)A whole (D)A fraction 2. [AS3] A fraction with denominator greater than numerator is called fraction. (A) An equivalent (B) A proper (C)An improper (D)A like EXERCISE 7.1. TYPES OF FRACTIONS 91

3. [AS3] Fractions with the same denominator are called fractions. (A) Llike (B) Unlike (C) Equivalent (D) Proper 4. [AS3] A fraction with its numerator greater than its denominator is called fraction. (A) A proper (B) An improper (C)A like (D)An unlike 5. [AS3] 6 and 6 are fractions. 13 11 (A) Like (B) Unlike (C) Equivalent (D) Improper 6 [AS5] Choose the correct answer. (i) To represent 2 on a number line, each division is sub–divided into equal parts. 5 (A) 1 (B) 2 (C) 5 (D) 10 [AS5] Answer the following questions in one sentence. (ii) Show 7 on a number line. 10 (iii) Show the fractions −3 , 6 and 13 on a number line. 11 11 11 (iv) Represent 3 on a number line. 5 (v) Represent 3 on a number line. 10 Short Answer Type Questions 7(i) [AS1] Convert the given mixed fractions into improper fractions. a) 2 3 b) 5 8 5 15 (ii) [AS1] Convert the following mixed fractions into improper fractions. (i) 6 3 (ii) 3 5 (iii) 51 2 10 11 3 EXERCISE 7.1. TYPES OF FRACTIONS 92

8(i) [AS1] Write each improper fraction as a mixed fraction. a) 63 b) 101 c) 209 10 9 12 (ii) [AS1] Write these improper fractions as mixed fractions. a) 48 b) 236 11 19 9 [AS1] Express these improper fractions as mixed fractions. (i) 15 (ii) 25 (iii) 32 (iv) 85 13 12 18 16 10(i) [AS1] Express these mixed fractions as improper fractions. a) 2 7 b) 7 4 9 13 (ii) [AS1] Express each of the following improper fractions as a mixed fraction. a) 23 b) 37 c) 50 5 6 7 11(i) [AS3] Identify the numerators and denominators of the following fractions: a) 12 b) −9 31 17 (ii) [AS3] Write fractions as indicated. a) Numerator: 4, Denominator: 7 b) Numerator:18, Denominator: 25 c) Numerator: (2)(–7), Denominator: (–3)(–5) 12(i) [AS3] Identify proper fractions from the following. 100 , 125 , 3 , 2 , 51 93 80 14 9 25 (ii) [AS3] Identify improper fractions from the following. 3 , 51 , 13 , 83 , 102 , 96 8 12 25 20 35 45 13(i) [AS3] Classify the following fractions as improper or mixed: 1 2 , 6 , 2 5 , 8 , 12 , 3 2 3 5 8 3 5 9 EXERCISE 7.1. TYPES OF FRACTIONS 93

14(i) [AS4] The length of femur, the longest bone in the human body is 101 cm. Express this length as 2 a mixed fraction. (ii) [AS4] Sujith bought 15 3 kg of wheat. How is the weight of wheat expressed as an improper 4 fraction? 15(i) [AS5] Write the fraction for the shaded part in the following figures. a) b) c) (ii) [AS5] Write the shaded parts of the following figures as fractions. a) b) c) EXERCISE 7.1. TYPES OF FRACTIONS 94

16(i) [AS5] Write the fractions for the shaded part in the following figures. a) b) (ii) [AS5] Draw circles, divide them into parts and shade them as per the given fractions. a) 2 1 b) 5 1 c) 1 2 3 4 3 Long Answer Type Questions 17 [AS3] Define the following: (i) Equivalent fractions (ii) Like fractions (iii) Unlike fractions (iv) Mixed fractions 18 [AS5] Write improper fractions to represent the shaded parts of the following figures. (i) (ii) (iii) (iv) (v) EXERCISE 7.1. TYPES OF FRACTIONS 95

19 [AS5] Divide the following figures into parts and shade them as per the fractions given. (i) 3 1 6 (ii) 2 3 8 (iii) 4 1 4 (iv) 1 5 8 (v) 2 2 5 EXERCISE 7.1. TYPES OF FRACTIONS 96

20 [AS5] Colour the Indian flag and write what fraction of the Indian flag the following colours are. (i) White (ii) Orange (iii) Green (iv) White and Green 21 [AS5] Show the following fractions on a number line. 2 , 0 , 4 , 6 , 13 , 4 2 5 5 5 5 5 5 22 [AS5] Represent the following like fractions on a number line. 1 2 , 1 1 , 1 5 , 1 3 , 1 9 10 10 10 10 10 23 [AS5] Represent 2 2 on a number line. 5 EXERCISE 7.1. TYPES OF FRACTIONS 97