202110719-PERFORM-STUDENT-WORKBOOK-MATHEMATICS-G06-FY_Optimized

11. Algebra • Use of Variable in Common Rules   Here ‘a’, ‘b’ are the length and breadth of the o Rules from Geometry rectangle.   1) Perimeter of a Square: Perimeter of a   If the perimeter of the rectangle is denoted by polygon is the sum of the length of its sides. the variable p, then A square has 4 sides and all sides are equal in length.   p = 2(a + b)   Perimeter of a square = S um of the lengths   Note that here ‘a’ and ‘b’ are both variables of the sides of a which can take values independent of each square other. = 4 times the length of side of the square   3) In geometry we will come across several such =4×a rules and formulae dealing with perimeter, = 4a area, surface areas, volume of 3-D figures, etc.   Rule for perimeter of a square = 4a where ‘a’ is Formulae may be obtained for sum of internal a variable. angles of a polygon, number of diagonals of a polygon, etc.   If perimeter is also represented by a variable o Rules for Arithmetic   1) Commutativity of addition of two numbers p, then p = 4a, i.e., the rule for perimeter of   a + b = b + a a square is expressed as a relation between   Here ‘a’ and ‘b’ are the variables which can take perimeter and length of the side of the square. •     2) Perimeter of a Rectangle any number (numerical) value.   Rectangle has 4 sides i.e., AB, BC, CD and DA.   Commuting is interchanging the order of Opposite sides of any rectangle are always equal in length. In rectangle ABCD, let us denote numbers. In addition, commutiation does not the length of sides AB and CD as ‘a’ and length change the sum. of sides BC and AD as ‘b’    Example: If a = 16 and b = 37   a + b = 16 + 37 = 53 and      b + a = 37 + 16 = 53   Perimeter of rectangle = Sum of length of all   ∴ a + b = b + a    2) Commutativity of multiplication of two sides of rectangle numbers = L ength of AB + Length of   Interchanging i.e., commuting the order of numbers in multiplication does not change the BC + Length CD + Length product value. of DA   a × b = b × a = 2 × length of AB + 2 ×   Here ‘a’ and ‘b’ are variables that can take any Lengtth of BC number (numerical) value. = 2a + 2b    Example: 10 × 16 = 160 = 2(a+b) 16 × 10 = 160 a × b = b × a    3) Associativity of addition of numbers   If a, b and c are 3 variables that can take any number (numerical) value, then   (a + b) + c = a + (b + c)    Example: (3 + 10) + 17 = 13 + 17 = 30 3 + (10 + 17) = 3 + 27 = 30 (a + b) + c = a + (b + c)   4) Distributivity of numbers   Let a, b and c be three variables which can take any number (numerical) value, then    a (b + c)= a × b + a × c 87

11. Algebra    Example: 6 × 59 = 6 × (50 + 9) o Using Expressions Practically = 6 × 50 + 6 × 9 = 300+ 54 Situations Variable Statement = 354 (Described in using ordinary language) expressions   Thus variables can be used effectively to Vijay’s father’s age Let Vijay’s Vijay’s father’s express the properties of numbers in a general is 5 years more than age is p age is (4p + 5) and concise manner. four times Vijay’s age. years. years • Expressions with Variables Price of tomato per Let price of Price of tomato Expressions with variables are obtained by applying kg is Rs. 9 less than Onion per per kg is Rs. the price of onion per kg be Rs. m (m – 9) operations of addition, subtraction, multiplication kg. and division on variables. Examples: 2n, (x + 15), (x – 8), etc The speed of car is Let speed Speed of car is The expression 2n is formed by multiplying the 30 km/hr more than of bus be (x + 30) km/hr. variable n with 2. the speed of a bus x km/hr. The expression (x + 15) is formed by adding 15 to going on the same variable x. road. • Variables do not have fixed values but they are also • Equation numbers. So, like numbers, operations of addition, An equation is a condition on a variable. It is subtraction, multiplication and division can be done on variables. expressed by saying that an expression with a variable is equal to a fixed number. o Formation of Expressions Example: 2n = 16 Expression How it is formed?   y + 7 = 18 8p + 7 First p is multiplied by 8 and then 7 Equation 2n = 16 , is satisfied only by the when the is added to the product. m m is divided by 12 value of the variable (n) is 8. Any other value of n 12 will not satisfy the equation. First y is multiplied by 13 and then Equation has an equal sign (=) between its two 13y – 5 5 is subtracted from the product. sides. The value of LHS (Left Hand Side) of the equation is o Writing Expressions from Statements equal to the value on the RHS (Right Hand Side) of the same equation. x is multiplied by 22 and then 3 is 22x + 3 If LHS is not equal to RHS, then the expression is added to the product. m – 31 not equation. 31 is subtracted from m. Example: 3n is greater than 16, is written as 3n > 15, This is not an equation. 3n is smaller than 25, i.e. 3n < 25 is not an equation. Consider 35 + 3 = 38. This is not an equation because LHS and RHS do not have variables and contain only numbers. This can be called numerical equation. • Solution of an Equation The value of the variable in an equation which satisfies the equation is called solution to the equation. Consider the equation 3x = 18, x = 6 satisfies the equation and no other value of x satisfies the 88

11. Algebra equation. So x = 6 is a solution of the equation 3x = 8. o Solution by Trial and Error Method   To find the solution to the equation, 3x = 18, prepare a table for various values of x and pick the value of x which is the solution to the equation. x 3x Condition Satisfied  Yes / No 13 No 26 No 39 No 4 12 No 5 15 No 6 18 Yes 7 21 No 8 24 No   Trial and error method is not a direct and practical way of finding a solution. o Direct Way / Systematic method of solving equations will be learnt in the next year. Work Plan COVERAGE DETAILS PRACTICE SHEET CONCEPT COVERAGE PS – 1 Algebra • Introduction PS - 2 • Idea of variables and of examples Self Evaluation Sheet • Use of variables in common rules • Expression with variables • Equations • Solution to the equations Worksheet for “Algebra” Evaluation with Self Check or ---- Peer Check* 89

PRACTICE SHEET - 1 (PS-1) 1. Find the rule which gives the number of 12. Find the solution for the following. matchsticks required to make the following i) x – 5 = 28 pattern using a variable. ii) 3p + 5 = 26 13. In an equation LHS = ------------- i) A pattern of letter P 14. Complete the table and by inspection of the ii) A pattern of letter M 2. A car travels 65 km in one hour. Express the table, find the solution to the equation 2x + 3 = 7 distance travelled by the car in terms of its travelling time in hours. x 12345 3. Arun is the father of Suma. Arun is 28 years older than Suma. Write Arun’s age in terms of 2x + 3 ? ? ? ? ? Suma’s age. 4. Gowri bought some number of chocolates to distribute among her classmates on her birthday. She distributed y number of chocolates to her classmates. After distributing, she was left with 17 chocolate with her. How many chocolates did Gowri buy? 5. The length of the sides of a regular octagon is ‘L’. Express the perimeter of octagon using ‘L’. 6. Explain the commutative and distributive property of addition of numbers using variables. Give examples. 7. Write the expression for the following cases. i) q is multiplied with –3 and 17 is added to the result. ii) 2 times of p from which three times of p is subtracted. iii) m is multiplied with 8 and then divided by 3 times n. 8. 3 (1 + 28) + 19 × 5 – 2 is a --------------- 3 expression. 9. What is a variable? Give an example. 10. Pavan’s present age is p years, i) What will be the Pavan’s age after 13 years? ii) What is Pavan’s daughter age if she is 28 years younger than Pavan? iii) What was Pavan’s age 7 years ago? 11. A car, bike and bus are moving from A to B. Bike has travelled a distance x km from A. Bus is 20 km behind bike and car is 13 km ahead of bike. What is the distance of bus and car from A. The total distance from A to B is 6 more than twice the distance of bike from A. Express the distance between A and B using x. 90

PRACTICE SHEET - 2 (PS-2) I. Choose the correct option. 1. In algebra, letters may stand for: (A) fixed quantities (B) known quantities (C) unknown quantities (D) Either A or B 2. ‘6 more than twice a number x’ can be written as: (A) 2x + 6 (B) 3x + 6 (C) 2x – 6 (D) 3x – 6 3. p – 6 is read as: (A) p decreased by 6 (B) 6 less than p (C) 6 taken away from p (D) All of these 4. The equation 3x = 9 is satisfied by the following value of x. (A) 2 (B) 3 (C) 4 (D) 9 5. The number of days in y weeks is: (A) 6y (B) 7y (C) 6x (D) 7x 6. The two-digit number with ten’s digit ‘p’ and unit’s digit ‘q’ is: (A) p + q (B) p – q (C) pq (D) P 7. The cost of one pen is Rs. x. If Ravi buy y pens. What is the cost of y pens? q (D) Rs`. xy (A) Rs. x + y (B) Rs. x – y (C) Rs. xy 8. There are x girls and y boys in a class. If each student has 8 books, then how many books are there in all with them? (A) 8 (x + y) (B) 8xy (C) 8 (x – y) (D) 8x + y 9. Which of the following equations does not have a solution in integers? (A) 3x + 5 = 7 (B) 2x +1 = 5 (C) x – 4 = 8 (D) 3x + 1 = 1 10. Think of a number and subtract 8 from it. If the difference is 32, then the equation can be written as: (A) x + 8 = 32 (B) x – 8 = 32 (C) x + 32 = 8 (D) x – 32 = 8 II. Short answer questions. 1. Count the number of line segments in each shape. (i) Write the rule for the above pattern. (ii) How many line segments will 8th shape contain? 2. Kiran’s age is half the age of her mother Sita. Calculate their ages in terms of x. (i) after 5 years (ii) before 6 years. 3. Write statement for each of the following expressions. (i) x + 6 (ii) x +2 3 III. Long answer questions. 1. Find the value of variable in the following equations by Trial and Error method. (i) 3y = 27 (ii) 5p – 12 = 38 2. Analyse and write the expressions for the following statements. (i) His grandfather’s age is 9 times of his age. (ii) The diameter (d) of a circle is twice its radius (r). (iii) Two-fifth of a number is 20. (iv) 11 subtracted from thrice a number gives 5. 91

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. There are 35 tomatoes in a bag. Write the total number of tomatoes if there are some bags 5. Change the following expressions into available. (1 Mark) ordinary language. i) An orange costs Rs. x. An apple costs Rs. 3x + 5 ii) Kiran’s age is m years. His wife is m – 5 years old.  (2 Marks) 2. Give expression for the following cases (i) 34 added to q (ii) -11 multiplied by q (2 Marks) 6. Justify that m = 6 is the solution of the equation 4m – 7 = 17 (2 Marks) 3. Write a rule which gives the number of match sticks required to make a pentagon pattern using variable. (2 Marks) 4. In the figure, O is the centre of the circle. XY 7. Find the solution of equation 5y = 25 by trial is diameter which is two times the radius of and error method. (3 Marks) the circle. Length of chord PQ is x. Find the perimeter of ∆POQ in terms of x and r. (3 Marks) 92

12. Ratio and Proportion Learning Outcome By the end of this lesson, a student will be able to: • Solve numerical (based on daily life situations) • Find rations of quantities. using unitary method. • Determine if the quantities are in proportion. Concept Map Key points example 24 in its lowest form = 3 i.e. 3:2. 16 2 • The common method adopted for comparing two quantities is to the difference between the two • Four quantities are said to be in proportion if the quantities. ratio of the 1st and the 2nd quantities is equal to the ratio of the 3rd and the 4th quantities. Thus • Another method of comparison is to divide two 3,2,12,8 are in proportion. First and fourth term are quantities i.e. By seeing how many times one known as extreme terms, second terms and third quantity is to the other quantity. This method is terms are known as middle terms called companion by ratio. • The order of terms in the proportion is important. 3,2,12 and 8 are in proportion but 2,3,12 and 8 are (a) for comparison by ratio, the two quantities must 2 12 be in the same unit. If not, they should be expressed not since 3 ≠ 8 in the same unit and then the ration is to be taken. • Unitary method: In this method, the value of one • The order in which quantities are considered to unit is determined first and then the value of express their ratio is important. 3: 2 and 2 : 3 are required number of units is determined. not the same. For example: (i) determine the cost of one book • Cost of 5 books = Rs.50 • Ratios may also be treated as fractions. The ratio • Then 1 book cost=s 55=0 Rs.10 2:3 may be treated as 2/3. ii) Determine cost of 3 books • Two ratios are equivalent, if the fractions Cost of 1 book Rs.10 corresponding to them are equivalent. Thus 3: 2 is ∴cost of 3books =Rs.10 × 3 equivalent to 6 : 4 or 12 : 8 Rs.30 • A ratio can be expressed in its lowest form. For 93

12. Ratio and Proportion Work Plan: CONCEPT COVERAGE DETAILS PRACTICE NO. OF COVERAGE SHEET PERIODS Ratio and Proportion Ratio PS – 1 04 Proportion PS - 2 02 Unitary method PS – 3 03 1 Worksheet for “Ratio and Proportion” PS - 4 1 Evaluation with Self ---- Self Evaluation Check or Peer Check* Sheet 94

PRACTICE SHEET - 1 (PS-1) 1. The ratio of 8 books to 10 books is 8. 2. The ratio of number of sides of a square to number of edges of a cube is? 3. A picture is 60 cm wide and 1.8 m long. Find the ratio of its width to its perimeter. 4. Neelam’s annual income is Rs.2,88,000 . Her annual savings amount to Rs.36000 . Find the ratio of her savings to the expenditure. 5. Mathematics textbook for class VI has 320 pages. The chapter on symmetry runs from page 261 to 272. Find the ratio of number of pages of this chapter to the total number of pages of the book? 6. In a box, the ratio of red marbles to blue marbles is 7:4. What is the total number of marbles in the box? 7. On a shelf, books with green cover and brown cover are in the ratio 2:3. If there are 18 books with green covers, find the number of books with brown cover. 8. There are ‘b’ boys & ‘g’ girls in a class. Find the ratio of number of boys to total no. of students. 9. The marked price of a table is Rs.625 and its sale price is Rs.500. What is the ratio of sale price to the marked price? 10. Reshma prepared 18 kg of barfi by mixing khoya with sugar in the ratio 7:2. How much khoya did she use? 11. A line segment 56 cm long is to be divided into 2 parts in the ratio 2:5. Find the length of each part. 12. Number of milk teeth in human beings is 20 and number of permanent teeth is 32. Find the ratio of number of milk teeth to number of permanent teeth. 13. In a year Ravi earns 3,60,000 and pays Rs 24,000 as income tax. Find the ratio of his. i. Income to income tax, ii. Income tax to income after paying income tax. 14. Rectangular sheet of paper is of length 1.2m and width 21cm. Find the ratio of width of paper to its length. 15. A scooter travels 120 km in 3 hours and train travels 120km in 2 hours. Find the ratio of their speeds. 16. An office opens at 9 AM and closes at 5:30 PM with a lunch break of 30 minutes. What is the ratio of lunch break to the total period in office? 95

PRACTICE SHEET - 2 (PS-2) 1. Determine if the following are in proportion: a. 4 : 7 and 20 : 35 b. 0.2 : 5 and 2 : 05 c. 3 : 33 and 33 : 3333 d. 15m : 40 m and 35 m : 65 m e. 27 cm2 : 57 cm2 and 18 cm : 38 cm f. 5 kg : 7.5 kg and Rs. 7.5 : Rs. 5 g. 20 g : 100 g and 1 m : 500 cm h. 12 hours : 30 hours and 8 km : 20 km i. 25 kg : 20 kg and 50 kg : 40 g 96

PRACTICE SHEET - 3 (PS-3) 1. A recipe calls for 1 cup of milk for every 2 cups of flour to make a cake that should feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people? 2. A car can travel 240 km in 15 litres of petrol. How much distance will it travel in 25 litres of petrol? 3. The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals. 4. Earth rotates 360° about its axis in about 24 hours. By how much degree will it rotate in 2 hours? 5. The quarterly school fee in a school for class VI is Rs.540. What will be the fee for seven months? 6. A metal pipe 3m long was found to weigh 7.6 kg. What would be the weight of the same kind of 7.8m long pipe? 1 7. A recipe for raspberry jelly calls for 5 cups of raspberry juice and 2 2 cups of sugar. Find the amount of sugar needed for 6 cups of the juice. 8. A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field? PRACTICE SHEET - 4 (PS-4) I. Choose the correct option. 1. The ratio of shaded parts to total number of parts of the figure is: (A) 4 : 1 (B) 1 : 4 (C) 4 : 5 (D) 1 : 5 2. If a, b and c are in proportion, then: (A) a : b : : c : a (B) a : b : : b : c (C) a : c : : b : c (D) a : b : : c : b 3. 3 : 8 is equivalent to: (A) 12 : 32 (B) 9 : 32 (C) 12 : 24 (D) 6 : 8 4. The simplest form of 36 : 42 is: (A) 6 : 7 (B) 2 : 3 (C) 4 : 7 (D) 6 : 8 5. The value of x if 4, 17, x, 51 are in proportion is: (A) 12 (B) 16 (C) 20 (D) 24 6. If 5 : 7 is equivalent to a : 35 then ‘a’ is: (A) 15 (B) 20 (C) 25 (D) 30 7. The length and breadth of a rectangle are in the ratio 5 : 4. If the breadth is 16 cm, then the length of the rectangle is: (A) 18 cm (B) 20 cm (C) 25 cm (D) 30 cm 8. The expenditure and savings of a person are in the ratio 5 : 7. If his savings are Rs. 700, then what is his expenditure? (A) Rs. 400 (B) Rs. 500 (C) Rs. 800 (D) Rs. 1000 9. Kiran bought 12 stickers for Rs. 144 and Rahi bought 8 stickers for Rs. 80. Who got the stickers cheaper and by how much per sticker? (A) Kiran by Rs. 2 (B) Rahi by Rs. 4 (C) Rahi by Rs. 2 (D) Kiran by Rs. 4 10. Rithu bought 9 marbles for Rs. 72 and Lucky bought 13 marbles for Rs. 117. Who got the marbles cheap- er and by how much per marble? (A) Rithu by Rs. 1 (B) Rithu by Rs. 3 (C) Lucky by Rs. 1 (D) Lucky by Rs. 3 97

PRACTICE SHEET - 4 (PS-4) II. Short answer questions. 1. 350 mg of maida and 500 mg of sugar are needed to make biscuits. Write the ratio of maida to sugar in lowest terms. 2. Rahul shared an amount of Rs.1600 between his son and daughter in the ratio of 3: 5. (i) What is the share of his son? (ii) What is the share of his daughter? 3. Here are 45 men and 60 women working in a workshop. Find the ratio of (i) men to women in the workshop (ii) men to the total number of employees (iii) women to the total number of employees III. Long answer questions. 1. Complete the following table. S. No First Quantity Second Quantity Ratio 1. 2. 3. 4. 2. A carton contains green and red apples. For every 3 green apples, there are 5 red apples. Complete this table based on the above information. (i) (ii) (iii) (iv) Green apples 6 24 Red apples 35 50 Total number of apples 98

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Cost of 4 dozen apples is Rs.180. How many 6. Ravi and Sheela started a business and invested apples can be purchased for Rs. 90? (2 Marks) money in the ratio 2:3. After one year the total profit was Rs.40,000. What are the shares of Ravi and Sheela in the profit? (3 Marks) 2. Find the ratio of areas of 2 circles if they have radius as 5 and 3 respectively. (2 Marks) 3. If x : 32 and 4 : 16 are equivalent ratio, then find the value of x. (1 Mark) 7. Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over and what is the ratio of their total runs made? (3 Marks) 4. Find the ratio of 20 minutes to 2 hours. (1 Mark) 5. In an examination which has questions of 100 marks. Aamir scores 54 marks while Usha loses 32 marks in her paper. Ratio of marks Aamir to that of Usha is same as that of marks obtained by Preeti and Kunal. If Preeti scored 72 marks, how much did Kunal score? (3 Marks) 99

13. Symmetry Learning Outcome By the end of this lesson, a student will be able to: • Identify symmetrical shapes • Identify lines of symmetry • Understand application of symmetry in daily life Concept Map Key points • Figures with evenly balanced proportions ae symmetric. • If there is line drawn, which can divide the figure into 2 identical parts, the line is called line of symmetry. • A figure can have no line of symmetry, one line of symmetry, 2 lines of symmetry or multiple lines of symmetry. • A scalene triangle has no line of symmetry. • An isosceles triangle has one line of symmetry. • A rectangle has 2 lines of symmetry. • An equilateral triangle has 3 lines of symmetry. • A Square has 4 lines of symmetry. • Line symmetry and mirror reflection are naturally related to each other with reflection, left < - > right changes in orientation has to be accounted for. 100

13. Symmetry Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET CSHymAmPeTtEryR: Quadratic EqSuyamtmioentrysand line of symmetry PS – 1 Two lines of symmetry PS – 2 PS - 3 Multiple lines of symmetry PS - 4 PS - 5 Reflection and symmetry Self Evaluation Sheet Worksheet for “Symmetry” Evaluation with Self Check ---- or Peer Check* 101

PRACTICE SHEET - 1 (PS-1) 1. How many lines of symmetry do the following figures have? 102

PRACTICE SHEET - 1 (PS-1) 2. Complete the figure such that the dotted line is the line of symmetry. 103

PRACTICE SHEET - 2 (PS-2) 1. How many lines of symmetry do the following figures have? 2. Complete the figure such that the dotted lines are the 2 lines of symmetry. a) c) b) d) 104

PRACTICE SHEET - 3 (PS-3) 1. How many lines of symmetry do the following figure have? a) f) b) h) c) d) e) 105

PRACTICE SHEET - 4 (PS-4) 1. Which of the following look the same after reflection? 106

PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. A line of symmetry is also known as ____________. (A) An axis of symmetry (B) A point of symmetry (C) A point of symmetry (D) A parallel line 2. Which of the following figures have the correct representation of lines of symmetry? (A) (B) (C) (D) 3. Which of the following letters have horizontal line of symmetry? (A) (B) (C) (D) 4. The number of lines of symmetry for the given figure is ______. (A) 1 (B) 2 (C) 0 (D) 3 5. The number of lines of symmetry for the letter A is ______. (D) 4 (A) 1 (B) 2 (C) 3 6. The number of lines of symmetry for the given figure is ____. (A) 0 (B) 1 (C) 2 (D) Many 7. A rhombus is symmetrical about _________. (A) Each of its diagonals (B) The line joining the midpoints of its opposite sides (C) The perpendicular bisectors of each of its sides (D) None of these 8. The mirror image of the given figure is ___________. (A) (B) (C) (D) 9. Which of the following letters do not have a line of symmetry (D) Both (A) and (B) (A) (B) (C) 107

PRACTICE SHEET - 5 (PS-5) 10. Which of the following is the mirror image of the given figure along the dotted line? (A) (B) (C) (D) II. Short Answer Questions. 1. Observe the given figures and find out the figures that are symmetrical. (i) (ii) (iii) (iv) 2. Draw mirror image of the given letters. (i) (ii) 3. Check whether the dotted line represents the line of symmetry or not. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) III. Long Answer Questions. 1. Define symmetry. List few objects that are in symmetry in your surroundings. 2. A figure can have no lines of symmetry and at the same time a figure can have countless lines of symmetry. Justify with examples. 108

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Define line of symmetry. 5. Complete the following by drawing mirror (1 Mark) images. (4 Marks) i) i) ii) ii) iii) iii) iv) iv) 2. In how many ways can the given figure be divided into 2 equal parts? (3 Marks) i) i) ii) ii) iii) iii) iv) iv) 3. Draw a polygon with lines of symmetry. What is it called? (3 Marks) 6. How many lines of symmetry does a regular polygon of n sides have?   (1 Mark) 4. How many lines of symmetry does the figure have? (3 Marks) 109

14. Practical Geometry Learning Outcome By the end of this lesson, a student will be able to: • Construct a perpendicular to a line through a point • Use the various tools for construction i.e., ruler, on it. compass, divider, set-squares and protractor. • Construct a perpendicular to a line through a point not on it. • Construct a circle where the radius is known. • Construct the perpendicular bisector of a line • Construct a line segment of given length. segment. • Construct a copy of a given line segment. • Construct an angle of a given measure. • Construct a copy of an angle of unknown measure. Concept Map Key points  On the line  Not on the line • Ruler, compass, divider, set squares and protractor o Perpendicular bisector of a line segment of are the mathematical instruments used for construction. given length o Angle of given measure and copy of an angle • Following constructions can be made using ruler o Bisector of a given angle and compass o Angles of special measure i.e, 30°, 45°, 60°, 90°, o Circle of known radium 120°, 135° o Line segment of given length o Copy of line segment o Perpendicular to a line through a point 110

14. Practical Geometry Work Plan: CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET PS – 1 Practical Geometry Introduction Construction of circle of known radius PS – 2 Line segment PS - 3 Construction of line segment of given length Construction copy of given line segment PS - 4 PS - 5 Perpendiculars:-through point on it, point not Self Evaluation Sheet on it, perpendicular bisector Angles-construct angle of given measure, construct copy of angle, bisector of angle. Angles of special measure Worksheet for “Practical Geometry” Evaluation with Self Check or ---- Peer Check* 111

PRACTICE SHEET - 1 (PS-1) 1. Draw a circle of diameter 7.6 cm. 2. Draw a circle of radius 3.5 cm. 3. Draw a circle of radius 5 cm, with the same centre draw two circle of radii 2cm and 3cm. 4. Draw a circle and show interior and exterior parts of circle. 5. Draw a circle of 7 cm radius. From any interior point of the circle, draw another circle passing through the centre of the first circle. 6. On a straight line of 9 cm, draw circles for every 3cm as radius. 7. Construct a circle with diameter 0.08 m. 112

PRACTICE SHEET - 2 (PS-2) 48152763........ DDCCCGGGCoooDrriiivvvaannneee.wwsssnnntttaarrrAAAuuunlBBBccciyntttioi,lessiAAfnAsooBBlBeeeffoognlloAfeefmgBflnnletlee.hggennnWttng5ghhtgitcttoht31mhhhf28oc7.11mcu.cC00m5tm.o.4cmcnC.,mmcCsofemtr.on.aroFnss.umrtuscortrtumtriahunctictgcshtoPcAipPQsBuyQct,wuooCwthffofohinAcfiABshfcCt.hAirsuCoistcfowt1lef/ai5nclecetgnohtogphfoty2hfAo.B35AfB..c3A.mBcm.. MaenadsBuDreoBfClength 2.7 cm. Measure 113

PRACTICE SHEET - 3 (PS-3) 1. Draw a perpendicular line to line segment AB using ruler and compass. 2. Draw CD⏊AB where C is a point on AB using ruler and compass. 3. Draw a perpendicular to XY using ruler and set square considering a point on XY. 4. Draw CD⊥ AB using ruler and set square considering a point C not on AB . 5. Draw AB of length 7cm and find axis of symmetry. 6. Draw AB of length 6.5 cm and find its arc’s of symmetry. 7. Draw a line segment of length 14 cm. Using compass, divide it into four equal parts. Verify by actual measurement. 8. Draw a circle whose diameter PQ is 7 cm. 9. Draw a circle of radius 5 cm. Draw any two of its chords. Construct the perpendicular biscetors of these chords. Where do they meet? 114

PRACTICE SHEET - 4 (PS-4) 1. Draw ∠ ABC of measure 85°. Find its line of symmetry. 2. Draw ∠PQR of measure 1540 . Find its line of symmetry. 3. Construct the following angles with ruler and compass i. 60° ii. 135° 4. Construct a right angle and bisect it. 5. Draw an angle of 50°. Make a copy of it using compass. 6. Draw an angle of 60°. Make a copy of its bisector using compass. 7. Construct angle 120° and divide into four equal parts using compass and ruler. 115

PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. Which of the following represents a line segment? (A) .P (B) (C) (D) 2. An angle is measured in _________. (A) Degrees (B) Litres (C) Metres (D)Kilograms 3. A line segment has ____ end points. (A) 1 (B) 2 (C) 0 (D) 3 4. If PQ = 9.5 cm and R is the mid-point of PQ, then QR = ____. (A) 4.75 (B) 4.5 (C) 4.25 (D) 4 5. A set of points in a plane which are at equidistance from a fixed-point forms a _____. (A) Square (B) Angle (C) Circle (D) Rectangle 6. A circle has ______ radii. (A) Two (B) Three (C) Four (D) Many 7. If you were asked to construct a circle, then which geometrical instrument do you use? (A) Compasses (B) Ruler (C) Protractor (D) Divider 8. If you were asked to construct an angle, then which geometrical instrument do you use? (A) Ruler alone (B) Both protractor and ruler (C) Divider (D) Protractor alone 9. Which of the following statements is true? (A) A point is a part of a line. (B) A ray is a part of a line (C) A line segment is a part of a line (D) All these 10. If AB = 8.2 cm and C is a point on AB and AC = 4.1 cm. Then C is called ____. (A) point above the line segment (B) mind point of AB (C) end point of AB (D) point below the line segment II. Short answer questions. 1. How many perpendicular lines can you draw for a given line segment? How many of them can be its perpendicular bisector?. 2. Draw a line segment of length 4.4 cm using a compasses. 3. Draw a line segment AB of length 9.2 cm. Mark a point C on it such that AC = 4.6 cm. Find BC. What can you say about point C? III. Long answer questions. 1. Define the terms: (i) Line segment (ii) Angle (iii) Perpendicular bisector of a line (iv) Angle bisector. 2. We can construct perpendicular bisector of a line using a ruler and compass. Justify. 116

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Draw a circle of diameter of 9.4 cm. From an interior point of circle draw another circle passing through the centre of the first circle. (3 Marks) 2. Given a line AB of length 6 cm. construct a line PQ which is twice of AB . (2 Marks) 3. Draw line segment AB of 5 cm. Find its axis of symmetry. (2 Marks) 4. Construct angle of 105° using compass. (3 Marks) 5. Draw an angle of 45° and make a copy of it using compass. (2 Marks) 6. Draw a circle of radius 3cm. Draw a chords and bisect it. (3 Marks) 117

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