Page 1 :
1, , Equal Triangles _ Worksheet 1.1, , STANDARD 8, , WORKSHEET, , 1.1, , Sides and angles, *, , *, , 1., , Two triangles are given below, a), Are the triangles equal? Why?, b), If the triangles are equal, which are the matching angles?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.1, , 2., , In triangles ∆ ABC and ∆ CDE, AC = EC, AB = DE, and, C is the midpoint of BD., a), Are the triangles equal? Why?, b), If the triangles are equal, which are the matching angles?, , 3., , In the figure ABCD is a square. Prove that ∆ ABC and ∆ ACD, are equal triangles., , 4., , In the quadrilateral ABDC, AB = BD, AC = DC., a), Are the triangles ∆ ABC and ∆ BCD, equal? Why?, b), If the triangles are equal, which are the, matching angles?, , 5., , In the figure, AB = DE, AC = CE, and C is the, midpoint of BD., a), Are the triangles equal? Why?, b), If∠B = 900, prove that AB and DE, are parallel., , Devapriya V Prabhu, TDHS, Mattancherry

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3, , Equal Triangles _ Worksheet 1.1, , 6., , In the figure, AD = AC, BD = BC., Write the matching angles of ∆ ABC and, ∆ ABD. Write the reason also., , 7., , In the figure, the two circles with centres A and B, are drawn with same radius., a), , Prove that the two triangles, ∆ ABC and ∆ ABD are equal., , b), , 8., , Also prove that the triangles are equilateral., , In the triangles ∆ ABC and ∆ DEF, all the angles are equal., Are the triangles equal? Why?, , *******************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equal Triangles _ Worksheet 1.2, , STANDARD 8, , WORKSHEET, , 1.2, , Two sides and an angle, *, , *, , 1., , If two sides and the included angle of one triangle, are equal to two sides and the included angle of, another triangle, then these two triangles are equal., , In the figure, AB = EF = 4 cm,, AC = DE = 6cm,∠A =∠E = 870, a), , Are these triangles equal? Why?, , b), , If the triangles are equal, write the, remaining equal sides and, matching angles., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.2, , 2., , In the figure, B is the midpoint of AE and CD., a), , Which are the equal sides in both, the triangles?, , 3., , b), , Write one pair of equal angles., , c), , Are the triangles equal? Why?, , d), , Prove that AC and DE are parallel., , From the figure, find the following., a), , Which are the equal sides?, , b), c), , Which are the equal angles?, Are the triangles ∆ ABC and ∆ DEF, equal? Why?, , 4., , In the figure, AD = BC. AD and BC are, perpendicular to AB. Prove that ∆ ABD and, ∆ ABC are equal triangles., , 5., , In the figure, AB = AD = 6 cm,, ED = FB = 2 cm, and∠A=900., a) Find AE and AF, b), Which are the equal sides in triangles, ∆ ADF and ∆ ABE ?, c), Are the triangles equal? Why?, , Devapriya V Prabhu, TDHS, Mattancherry

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3, , Equal Triangles _ Worksheet 1.2, , 6., , In the figure, AH = BH = DH = EH = 4 cm, and ∠AHB = ∠EHD = 600., a), , prove that AB = DE, , b), , also prove that ∆ HDE and ∆ HAB are, equilateral triangles., , 7., , In the figure G is the midpoint of EF, and HG is perpendicular to EF., a), , Are the triangles ∆ EGH and ∆ FGH, equal? Why?, , b), , If H is the midpoint of AB, and, quadrilateral ABFE is a rectangle, prove that ∆ EAH and ∆ FBH are equal., , 8., , In the figure, AB = 5cm, BC = BD = 3 cm,, , ∠A=300. Are ∆ ABC and ∆ ABD equal? Why?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equal Triangles _ Worksheet 1.3, , STANDARD 8, , WORKSHEET, , 1.3, , One side and two angles, *, , *, , 1., , If one side and two angles on it of one triangle are equal to, one side and two angles on it of another triangle, then the, triangles are equal., , In the figure,, a), , are the triangles ∆ ABC and, ∆ CDE equal? Why?, , b), , what is the measure of the remaining, angle in the triangles?, , c), , which are the matching sides, in the triangles?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.3, , 2., , In the quadrilateral ABCD, AB is parallel to DC, and AD is parallel to BC., , 3., , a), , Prove that ∆ ABC and ∆ ADC are equal., , b), , Also prove that AB = CD and AD = BC., , The quadrilateral ABCD is a parallelogram., a), , Prove that AE = CE and BE = DE., , b), , What is the speciality of the point E, with respect to the diagonals AC and BD?, , 4., , In the figure, G is the midpoint of DE., a), , What is the measure of∠D?, , b), , What is the measure of∠BGE?, , c), , Are the triangles ∆ ADG and ∆ BFG, equal? Why?, , d), , 5., , Prove that G is the midpoint of AB also., , In the figure, AB = DF = 4 cm, Two angles are, given in each triangle., a), Find the third angle in each triangle., b), , Are the triangles equal? Why?, , c), , If they are equal, Find the matching pairs, of sides in both the triangles., , Devapriya V Prabhu, TDHS, Mattancherry

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3, , Equal Triangles _ Worksheet 1.3, , 6., , In the figure, AF and DE are parallel and, DE and BF are equal., a), , Write the matching angles of ∆ BFG, and ∆ DEG, , b), , Are the triangles ∆ BFG and, and ∆ DEG equal? Why?, , 7., , In the figure, ABDC is a parallelogram., F is a point on the line AB extended., CE and DF are perpendicular to AF., , E, , a), , Which are the matching angles in the triangles, ∆ AEC and ∆ BFD?, , b), , 8., , Prove that ∆ AEC and ∆ BFD are equal., , In the quadrilateral ABED, the quadrilaterals, ADEF and BEDF are parallelograms., F is the midpoint of AB. Prove that the triangles, ∆ ADF, ∆ DEF and ∆ BEF are equal., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.4, , 1., , In ∆ ABC, AC = BC = 5 cm and AB = 6 cm., D is the midpoint of AB., a), Are the triangles ∆ACD and ∆BCD equal? Why?, b), Prove that CD is perpendicular to AB., c), Find CD, d), Find the area of ∆ ABC, , 2., , What is the area of an isosceles triangle with base 8 cm, and the equal sides 5 cm?, , 3., , In the figure, AC = BC = 4 cm and∠DBC = 126°., Find all the angles of ∆ ABC., , 4., , In ∆ ABD, AD = BD and ∠BDE = 70°., Find ∠ADB and∠ABD, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equal Triangles _ Worksheet 1.5, , STANDARD 8, , WORKSHEET, , 1.5, , EXTRA QUESTIONS, 1., , In the figure, ABCDE is a pentagon in which all, sides are equal and all angles are equal., , 2., , a), , Are the triangles ∆ ADE and ∆ BDC equal? Why?, , b), , Prove that ∆ ABD is an isosceles triangle., , In figure ABCDEF is a hexagon in which all sides, are equal and all angles are equal., a), , Are ∆ AFE and ∆ BCD equal? Why?, , b), , If ∠F = 120°, find all the angles of ∆ BCD., , c), , Find all angles of the quadrilateral ABDE., , d), , Write a suitable name for quadrilateral ABDE., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.5, , 3., , ∆ ABC is an equilateral triangle. D, E, F are, the midpoints of the sides AB, BC, AC respectively., , 4., , a), , How many triangles are there in the figure?, , b), , Prove that all small triangles are also equilateral., , c), , Also prove that all small triangles are equal., , In the figure, O is the centre of the circle and, ∠BOC=80°., , 5., , a), , Find∠AOC, , b), , Find∠OAC, , c), , If∠BOC =100°,find∠OAC, , d), , What is the relation between∠BOC and ∠OAC?, , In the figure, O is the centre of the circle and, ∠BOC = 64°, a), , Find all the angles of ∆ BOC, , b), , Find all the angles of ∆ AOC, , c), , Calculate ∠ACB, , d), , If ∠BOC = 50°, find∠ACB., , e), , Write the speciality of angle∠ACB using, above measures., , *****************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equal Triangles _ Worksheet 1.6, , STANDARD 8, , WORKSHEET, , 1.6, , CONSTRUCTIONS, *, , *, , A line dividing a line or an angle into two equal parts is, called a bisector., , *, , When the bisector is perpendicular to the given line, then, it is called the perpendicular bisector of the line., , 1., , Draw a line 7.5 cm long and draw its perpendicular bisector., , 2., , Draw a square of each side 3.25 cm., , 3., , Draw a square of each side 4.25 cm, , 4., , Draw a circle of radius 3.75 cm., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equal Triangles _ Worksheet 1.6, , 5., , Draw a circle of diameter 5.5 cm., , 6., , Draw an equilateral triangle of side 4.75 cm., , 7., , Draw an isosceles right angled triangle with equal sides 4.25 cm., , 8., , Draw 45° and 22 1 ° angles using compass and scale., , 9., , Draw 60°, 30°, 15° angles without using protractor., , 10., , 1, Draw ∆ABC in which AB = 5 cm, ∠A = 22 ° and ∠B = 60°, , 2, , 2, , without using protractor., , 11., , 1, Draw ∆ABC in which AB = 6cm, ∠A = 22 ° and ∠B= 90°, 2, , without using protractor., , 12., , 1, Draw ∆ABC in which AB = 6cm, ∠A = 67 ° and ∠B= 45°, 2, , without using protractor. What is the speciality of this triangle?, , ***************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equations _ Worksheet 2.1, , STANDARD 8, , WORKSHEET, , 2.1, , Addition and Subtraction, *, , 1., , Balu got 600 rupees as gift for his birthday., He went to shop and purchased some sporting goods., Now he had 301 rupees left with him. How much did he spend?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equations _ Worksheet 2.1, , 2., , Ganesh has some books in his library., He says that if he had 54 books more,, then he would have 250 books., How many books Ganesh has in his library now?, , 3., , Malini found 78 seashells on the beach., She gave some of them to her friend., Now she has 46 seashells with her., How many seashells did she give to her friend?, , 4., , When 212 is added to a number, makes it 750., What is the number?, , 5., , When 164 is subtracted from a number, makes it 235., What is the number?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equations _ Worksheet 2.2, , STANDARD 8, , WORKSHEET, , 2.2, , Multiplication and division, *, , 1., , The price of 4 shirts is 720 rupees., What is the price of one shirt?, , 2., , The age of Raju’s father is 9 times that of Raju., If the father’s age is 36 years, what is Raju’s age?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equations _ Worksheet 2.2, , 3., , Six friends equally divided the total profit they got, from a business. If one of them got 1275 rupees,, what was their total profit?, , 4., , Eight people divided the amount for a show among them., What was the ticket rate if the total amount was 1120?, , 5., , A number when multiplied by 14 gives 1008., What is the number?, , 6., , A number when divided by 41 gives 215., What is the number?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equations _ Worksheet 2.3, , STANDARD 8, , WORKSHEET, , 2.3, , Different Changes, *, , 1., , One is added to three times of a number gives 100., What is the number?, , 2., , The double of 3 less than a number is 100., What is the number?, Devapriya V Prabhu, TDHS, Mattancherry

Page 22 :
2, , Equations _ Worksheet 2.3, , 3., , Two less than three times a number is 100., What is the number?, , 4., , 10 is added to half of a number gives 100., What is the number?, , 5., , The half of 2 less than a number is 100., What is the number?, , 6., , The perimeter of a rectangle is 24 cm and one side is 4 cm., Find the other side., , 7., , The number of boys in a class is 3 more than twice, the number of girls. If the number of boys is 31,, find the number of girls., , 8., , Aalia has Rupees 150 which is 8 rupees more than twice, what Aadil has. How much has Aadil?, , ***************, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equations _ Worksheet 2.4, , 2., , The perimeter of a rectangle is 46cm., The length is 5cm more than the breadth., What are its length and breadth?, , 3., , The second angle of a triangle is double the first., The third angle is 40 less than the first., Find the three angles., , 4., , The sum of three consecutive natural numbers is 93., What are the numbers?, , 5., , The sum of three consecutive even numbers is 246., What are the numbers?, , ***************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equations _ Worksheet 2.5, , STANDARD 8, , WORKSHEET, , 2.5, , Colendar problems, *, , 1., , In a square of four numbers from a calendar one number is given., Write appropriate numbers in the place of question marks., , 17, , ?, , ?, ?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Equations _ Worksheet 2.5, , 2., , In a square of nine numbers from a calendar,, one number is given. Write appropriate numbers, in the place of question marks., , 3., , ?, , ?, , ?, , ?, , 19, , ?, , ?, , ?, , ?, , In a calendar, a square of four numbers is marked., The sum of the numbers is 100. What are the numbers?, , 4., , A square of nine numbers is marked in a calendar., The sum of all these numbers is 189. What are the numbers?, , 5., , If a = 1, b = 2, c = 3, ..... z = 26, then replace the question, marks in the square from the calendar with suitable letters., , ?, , ?, , ?, , ?, , q, , ?, , ?, , ?, , ?, , *****************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Equations _ Worksheet 2.6, , STANDARD 8, , WORKSHEET, , 2.6, , Different Problems, *, , 1., , 3 added to 2 times the number, and 2 added to 3 times the, number gives the same result. What is the number?, , 2., , Fourteen less than eight times a number is two more than four, times the number. What is the number?, , Devapriya V Prabhu, TDHS, Mattancherry

Page 28 :
2, , Equations _ Worksheet 2.6, , 3., , Eleven less than seven times a number is five more than six, times the number. Find the number., , 4., , Fifteen more than three times a number is the same as twelve, less than six times the number. What is the number?, , 5., , Sixty more than nine times a number is the same as two less, than ten times the number. What is the number?, , Devapriya V Prabhu, TDHS, Mattancherry

Page 29 :
1, , Equations _ Worksheet 2.7, , STANDARD 8, , WORKSHEET, , 2.7, , Different Problems, *, , 1., , Fifteen years from now Rahul’s age will be four times, his present age. What is Rahul’s present age?, , 2., , A grand father is 10 times older than his grand daughter., Also he is 54 years older than her. Find their present ages?, Devapriya V Prabhu, TDHS, Mattancherry

Page 30 :
2, , Equations _ Worksheet 2.7, , 3., , Three fourth of a number is 2 more than one fourth of a, number. Find the number., , 4., , Seven times a number is 36 less than 10 times the number., Find the number., , 5., , If, , 3, 5, , of a number is 4 more than 1 the number,, 5, , then what is the number?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Polygons_ Worksheet 3.1, , STANDARD 8, , WORKSHEET, , 3.1, , SUM OF ANGLES, , 1., , Complete the table suitably, FIGURE, , NUMBER, OF SIDES, , NUMBER OF, TRIANGLES, , SUM OF ANGLES IN THE, POLYGONS, , 3, , 3–2=1, , (3-2) x 180º, = 1 x 180º = 180º, , 4, , 4–2=2, , (4 – 2) x 180º, , TRIANGLE, , =.......... = 360º, , QUADRILATERAL, , (5 – 2) x 180º, 5, , .......... = 3, = 3 x 180º = .........., , PENTAGON, , 6, , .......... = 4, , (6 – 2) x 180º, = .......... = .........., , n, , .........., , .........., , HEXAGON, , ‘n’ sided, polygon, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Polygons_ Worksheet 3.1, , 2., , What is the sum of angles of a polygon with sides 102?, , 3., , What is the sum of angles of a 22 sided polygon?, , 4., , The sum of angles of a polygon is 6300º. How many, sides does it have?, , 5., , The sum of angles of a polygon is 10440º. Then, a), , The sum of angles of a polygon with one more side, = 10440 +...... = ......., , b), , The sum of angles of a polygon with one side less, = 10440 - ...... = ......., , 6., , The number of triangles formed by drawing diagonals, from one vertex of a polygon is 18. Then, , 7., , a), , what is the sum of angles of the polygon?, , b), , what is the number of sides of the polygon?, , In the traffic sign,, a), , how many sides are there for the polygon?, , b), , how many diagonals can we draw from one vertex?, , c), , how many triangles can we form using diagonals?, , d), , what is the sum of angles of this polygon?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Polygons_ Worksheet 3.2, , STANDARD 8, , WORKSHEET, , 3.2, , Outer angles, “THE INNER ANGLE, AND OUTER ANGLE, AT EACH VERTEX, OF ANY POLYGON, FORM A LINEAR PAIR.”, , 1., , Compute all outer angles and inner angles of the triangle., , 2., , Compute all outer angles and inner angles of the quadrilateral., , Devapriya V Prabhu, TDHS, Mattancherry, , Got the idea!!, Inner angle, +Outer angle, =180º

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2, , Polygons_ Worksheet 3.2, , 3., , Compute the angles in the place of the, question mark in the figure., , 4., , Find x from the figure, , 5., , Find x and compute all outer angles and inner angles of the triangle, , 6., , Compute all outer angles and inner angles of the quadrilateral., , 7., , From the figure,, a), find∠BAC, b), find∠ACB, c), find the relation between, the inner angles ∠BAC and ∠ABC, and the outer angle ∠ACD?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Polygons_ Worksheet 3.3, , STANDARD 8, , WORKSHEET, , 3.3, , Unchanging sum, *, Got the idea!!, Inner angle +, Outer angle, =180º, , 1., , 2., , 3., , All angles of a polygon are equal. One outer angle is 36º., a), , Find the number of sides of the polygon., , b), , Find the sum of inner angles., , ., , All angles of a polygon are equal. One inner angle is 165º., a), Find one outer angle of the polygon., b), , Find the number of sides of the polygon., , c), , Find the sum of angles of the polygon., , In the figure, two angles of the pentagon are 90º., a), , Find x, , b), , Find the marked outer angle, , c), , If all angles are equal, then what is the, measure of one outer angle?, Devapriya V Prabhu, TDHS, Mattancherry

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2, , Polygons_ Worksheet 3.3, , 4., , In the figure, AB is parallel to DC., a) find ∠BAD, b) find x, c) find all inner angles, d) find all outer angles, , 5., , In the figure, AB is parallel to DC., a), , find all inner angles of the, quadrilateral ABCD., , b), , find all outer angles of the, quadrilateral ABCD., , “My lord...., Your inner angle, is my outer angle, which is equal to, 180 minus your outer angle., Can you tell me, Your outer angle?”, , 38º, , Devapriya V Prabhu, TDHS, Mattancherry, , “Tell me what is the, Measure of, Your Outer angle?, Otherwise, I will eat you”, Can you, help me, Dear children?, I won’t, eat him.

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1, , Polygons_ Worksheet 3.4, , STANDARD 8, , WORKSHEET, , 3.4, , Regular Polygons, , 1., , One angle of a regular polygon is 156°., a), , What is one outer angle?, , b), , What is the number of sides of the polygon?, , Devapriya V Prabhu, TDHS, Mattancherry, , Don’t forget!!, Inner angle +, Outer angle, =180º

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2, , Polygons_ Worksheet 3.4, , 2., , 3., , 4., , One outer angle of a regular polygon is 20°., a), , What is the number of sides of the polygon?, , b), , What is one inner angle of the polygon?, , c), , What is the sum of the inner angles?, , a), , How much is one outer angle for a 24 sided regular polygon?, , b), , How much is its one inner angle?, , c), , What is the sum of the inner angles?, , Check whether the following are outer angles of regular, polygons or not. If they are outer angles, find, the number of sides also., a), , 5., , 5°, , b), , 11°, , c), , 8°, , d), , 14°, , The sum of all angles of a regular polygon is 2880°., a), , What is the number of sides of the polygon?, , b), , What is one outer angle?, , c), , What is one inner angle of the polygon?, , ****************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Polygons_ Worksheet 3.5, , STANDARD 8, , WORKSHEET, , 3.5, , Regular Polygons, , 1., , Two regular pentagons are put together, as shown in the figure. Find ∠ABC., , Devapriya V Prabhu, TDHS, Mattancherry, , Don’t forget!!, Sum of angles, around a point, =360º

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2, , Polygons_ Worksheet 3.5, , 2., , Three regular pentagons are put together, as shown in the figure. Find ∠ABC., , 3., , In the figure, a square and two regular pentagons put together., Find, , 4., , a), , ∠ABF, , b), , ∠DCG, , In the figure, a regular hexagon, a regular pentagon and an, equilateral triangle put together., Find, , 5., , a), , ∠BAC, , b), , ∠DEF, , In the figure, a regular hexagon, a regular pentagon, a square, and an equilateral triangle put together. Find, a), , ∠CAO, , b), , ∠DEQ, , c), , ∠NLK, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Polygons_ Worksheet 3.6, , STANDARD 8, , WORKSHEET, , 3.6, , Regular Polygons, , 1., , ABCDEF is a regular hexagon. Prove that all the triangles, formed are equilateral triangles., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Polygons_ Worksheet 3.6, , 2., , ABCDEF is a regular hexagon., a), , What is the measure of each angle, in a regular hexagon?, , 3., , b), , What type of triangle is ∆ BCD?, , c), , Find all angles of ∆ BCD., , d), , What type of triangle is ∆ BDE?, , e), , Find all angles of ∆ BDE., , f), , Find all angles of the quadrilateral ABEF., , ABCDEF is a regular hexagon., Prove that all sides of the two, quadrilaterals AHEF and BCDH, are equal. Also find all its angles., , 4., , In the figure, ABCDEF is a, regular hexagon. Prove that, the sum of all the marked, angles is 360º., , 5., , A geometrical pattern is made, using regular polygons., a), , Which are the regular polygons, needed to complete this pattern?, , b), , How many regular polygons are, needed to complete this pattern?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Identities_ Worksheet 4.1, , STANDARD 8, , WORKSHEET, , 4.1, , Identity Using Geometry, 1., , In the figure, two rectangles ABCD, and BEFC are attached together., If AB = x cm, BE = y cm, AD = z cm,, a), , What is the area of the rectangle ABCD ?, , b), , What is the area of the rectangle BEFC ?, , c), , What is the length of the rectangle AEFD?, , d), , What is the breadth of the rectangle AEFD?, , e), , Then what is the area of the rectangle AEFD ?, , f), , What is the sum of areas of rectangles ABCD and BEFC?, Devapriya V Prabhu, TDHS, Mattancherry

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2, , Identities_ Worksheet 4.1, , g), , What is the relation between the area of the rectangle AEFD, and the sum of areas of rectangles ABCD and BEFC?, , h), 2., , Write the relation as an equation., , Four friends are describing their plots. Help them to find the, area of their plots. All are rectangular plots., , Then, a), , the area of plot I = ( 24 x .....), , b), , the area of plot II= (...... x 11), , c), , the area of plot III = ( 22 x .....) d), , e), , length of the largest rectangular plot = ..... + 22 = ......., , f), , breadth of the largest rectangular plot = 11 + ..... = ......, , g), , area of the largest rectangular plot = ...... x ....., , h), , Can you write the relation between the area of the largest, , the area of plot IV= (..... x .....), , rectangle and the sum of areas of the four smaller rectangles, using the hints?, 46 x 17 = (24 +....) (11 +...) = (24 x ....)+ (.... x ....) + (22 x ....) + (.... x 6), = ......... + ........ + ......... + ........., = ......... m2, Devapriya V Prabhu, TDHS, Mattancherry

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3, , Identities_ Worksheet 4.1, Do like this..., 26 x 34 = (20 + 6)(30 +4), = (20 x 30) + (20 x 4) + (6 x30), + ( 6 x 4), = 600 + 80 + 180 + 24, = 884, , 3., , Find the products using the given Identity, , (x + y) (u + v) = xu + xv + yu + yv, i), , 46 x 68 = (40 + 6) (60 + 8) = ...................., , ii), , 54 x 73 = ...................., , iii), , 102 x 105 = ( 100 + .... ) ( 100 + .... ) = ...................., , iv), , 103 x 204 = ...................., , v), , 105 x 107 = ...................., , vi), , = ...................., , vii), , = ...................., , **************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Identities_ Worksheet 4.2, , STANDARD 8, , WORKSHEET, , 4.2, , PRODUCT OF SUMS, 1., , Look at the table below., , a), , 1, , 2, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , 10, , 11, , 12, , 13, , 14, , 15, , 16, , 17, , 18, , 19, , 20, , 21, , 22, , 23, , 24, , 25, , 26, , 27, , 28, , 29, , 30, , Mark four numbers in a square and find the difference, of diagonal products., Devapriya V Prabhu, TDHS, Mattancherry

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2, , Identities_ Worksheet 4.2, , b), 2., , 3., , Explain why this is so, using algebra., , From the above table, take a square of 9 numbers and mark, the numbers at the four corners., a), , Find the difference of diagonal products., , b), , Explain why this is so, using algebra., , Find the products of the given numbers using the identity, (x + 1)(y + 1) = x y + (x + y) + 1, Dears...., do like, This!, , *Example: 21 x 41 = (20 + 1)(40 + 1), , = 20 x 40 + 20 x 1 + 1 x 40 + 1 x 1, = 800 + ( 20 + 40 )+ 1, = 800 + 60 + 1 = 861, , 4., , a), , 31 x 51, , = ( 30 + ... )( 50 + ... ), = 30 x 50 + ( 30 + 50 ) + 1 = ......., , b), , 21 x 71, , = ......., , c), , 101 x 201 = ......., , Find the products of the given numbers using the identity, (x + 2)(y + 2) = x y + 2x + 2y + 4 = x y + 2 (x + y) + 4, Try like this..., , *, , Example: 22 x 42 = (20 + 2)(40 + 2), = 20 x 40 + 20 x 2 + 2 x 40 + 2 x 2, = 800 + (40 + 20) x 2 + 4, = 800 + 60 x 2 + 4, = 800 + 120 + 4 = 924, , Devapriya V Prabhu, TDHS, Mattancherry

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3, , Identities_ Worksheet 4.2, , a), , 12 x 62, , = (10 + ...)(60 + ...) = 10 x 60 + ( ... + ...) x 2 + ....., = ......., , 5., , b), , 42 x 82, , =, , c), , 102 x 202 =, , If 50 x 60 = 3000, calculate in head the products of the following, a), , 51 x 61, , b), , 52 x 62, , c), , 54 x 64, , d), , 57 x 67, , ****************, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Identities_ Worksheet 4.3, , STANDARD 8, , WORKSHEET, , 4.3, , Square of a Sum, *, , GEOMETRICAL EXPLANATION TO THE IDENTITY, Length of large square = (x+y), Breadth of large square = (x+y), ∴ Area of large square = (x+y)(x+y), = (x+y)², Sum of all areas inside the large, Square of a Sum, square = x² + xy + yx + y², ∴ (x + y)² = x² + 2xy + y², 1., , Compute the squares of the following numbers using the identity., i), , 2., , 85², , ii), , 106² iii), , 202² iv), , 10.3² v), , Study the following pattern. Write three more lines and explain using algebra., , 2² + (2 + 2 + 1) = 9 = 3², 3² + (3 + 3 + 1) = 16 = 4², 4² + (4 + 4 + 1) = 25 = 5², ......................................., ......................................., Devapriya V Prabhu, TDHS, Mattancherry

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2, , Identities_ Worksheet 4.3, , 3., , Study the following pattern. Write three more lines., 3² = 9 = 4 x 1 x 2 + 1, 5² = 25 = 4 x 2 x 3 + 1, 7² = 49 = 4 x 3 x 4 + 1, ....................................., ......................................, , 4., , Aren’t they, Interesting, friends?, , Study the following pattern. Write two more lines., 3² = 9 = 8 x 1 + 1, 5² = 25 = 8 x (1+2) + 1, 7² = 49 = 8 x (1+2+3) + 1, 9² = 81 = 8 x (1+2+3+4) + 1, ....................................., ....................................., , 5., , Given the method of calculating 46²., Example: 46², 4² = 16, , 16 x 100 = 1600, , 1600, , 2 x (4 x 6)= 48, , 48 x 10 = 480, , 480, , 6² = 36, , 36 x 1, , 36, , 46², , Check the method for, , 2116, , i), , 53², , ii), , 87², , Dears...., don’t forget!!, , (a+b)² = a²+b²+2ab, , Devapriya V Prabhu, TDHS, Mattancherry, , Do, like this!!

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1, , Identities_ Worksheet 4.4, , STANDARD 8, , WORKSHEET, , 4.4, , Product of differences, *, , *, *, , *, , Friends..., Do using this, Example!, , *Eg: 298 x 199 = (300-2)(200-1), , = (300 x 200) – (300 x 1) – (2 x 200) + (2 x 1), = 60000 – 300 – 400 + 2 = 59302, 1., , Find the product of the following numbers using identity., a), , 299 x 198, , b), , 397 x 196, , c), , Devapriya V Prabhu, TDHS, Mattancherry, , 399 x 297

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2, , Identities_ Worksheet 4.4, , Examples, 97² = (100 – 3)², = 100² - (2 x 100 x 3)+ 3², = 10000 – 600 + 9, = 9409, , (9 3 )² = (10 - 1 )², 4, , 4, , = 10 ² – 2 x 10 x 1 + ( 1 )², = 100 – 5 +, = 95 1, , 1, 16, , 4, , 16, , 2., , Compute the squares of the following numbers using identity., a), , 3., , 96², , b), , 199², , c), , (19, , 1, )², 4, , Study the pattern and write two more similar rows., 3² – 4 x 2 x 1 = 1², 5² – 4 x 3 x 2 = 1², 7² – 4 x 5 x 2 = 3², 10² – 4 x 6 x 4 = 2², 13² – .............. = ...., ......................................, , 4., , Study the pattern and write two more similar rows., 2² + 4 x 3 x 1 = 4², 3² + 4 x 6 x 3 = 9², 4² + 4 x 7 x 3 = 10², 5² + 4 x 6 x 1 = 7², , I think there is a, connection, Between, (x+y)² and (x-y)², , 10² + 4 x ....... = ...., ................................, , Devapriya V Prabhu, TDHS, Mattancherry, , 4

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1, , Identities_ Worksheet 4.5, , STANDARD 8, , WORKSHEET, , 4.5, , Sum and difference, *, , *, *, , *, Friends..., Do using these, Examples!, , Eg:, , *203 x 298 = (200+3)(300-2), , = (200 x 300) – (200 x 2) + (3 x 300) – (3 x 2), = 60000 – 400 + 900 - 6 = 60494, , 1., , Find the product of the following numbers using identity., a), , 202 x 299, , b), , 301 x 397, , c), , 103 x 198, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Identities_ Worksheet 4.5, , Eg:, 205 x 195 = (200 + 5)(200 – 5), = 200² - 5², = 40000 – 25, = 39975, =, , 2., , Find the product of the following numbers using identity., a), , 106 x 94, , b) 202 x 198, , c), , *, , Reverse of the Identity: x² – y² = (x+y)(x-y), , Eg:, 3., , Find the difference of the given squares using identity, a), , 199² – 198², , b) 186² – 184², , c), , (26.5)² – (23.5)², Friends ..., don’t be confused..., See the examples ..., And then do..., , Eg:, , 4., , Write the given numbers as the difference of two squares, a), , 15, , b), , 33, , c), , 41, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Identities_ Worksheet 4.6, , STANDARD 8, , WORKSHEET, , 4.6, , MORE IDEAS, *, , Friends...please read, Then answer..., , Any odd number greater than 1 can be written as the, , difference of consecutive perfect squares., * All multiples of 4, starting with 8, can be written, as the difference of two perfect squares., , Eg:, , 9, , = 5² - 4², , * 1,4, and 2,6,10,14,18, 22, .....can, not be written as the, ....., difference of two perfect squares., * That is 1,4 and numbers leave remainder 2 on division by 4, can not be written as the difference of two perfect squares., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Identities_ Worksheet 4.6, , *Eg: Can 309 be written as the difference of two perfect squares?, 309 is an odd number. So 309 can be written as the difference of, two consecutive perfect squares., 309 = 309 x 1 = (155+154)(155-154) = 155² - 154², Also 309 = 103 x 3 = (53+50)(53-50) = 53² – 50², *Eg: Can 4002 be written as the difference of two perfect squares?, When 4002 is divided by 4, the remainder is 2. So 4002 can not be, written as the difference of two perfect squares., Divide each, Number by 4, And check the, Remainder...., , 1., , Which of the following numbers can be written as the difference, between two perfect squares?, a), , 2., , 218, , b), , 436, , c), , 1234, , d), , Write the following numbers as the difference between two perfect squares, a), , 80, , b), , 95, , c), , 121, , *, , *, , Reverse of the Identity: x² – y² = (x+y)(x-y), , *, , We know that, 10² – 9² = (10+9)(10-9) = 19 x 1, That is,, 10² – 9² = 10+9 = Sum of numbers, and, 10² – 8² = (10+8)(10-8) = 18 x 2, That is,, 10² – 8² = (10+8) x 2 = Two times their sum, Similarly,, 10² – 7² = (10+7)(10-7) = 17 x 3, That is,, 10² – 7² = (10+7) x 3 = Three times their sum, , 3., , 2020, , Using any two numbers write some steps like those in the, example and explain the relation between the difference of, squares of two natural numbers and their sum., , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Money Maths _ Worksheet 5.1, , 1. Anu deposited an amount of Rs. 10000 in a bank which compounded, interest at the rate 8% annually. How much amount would she, get after 2 years?, 2. Appu took out a loan of 20000 rupees from a bank which charges 12%, interest compounded annually. To settle the loan how much should he, pay at the end of 3 years?, 3. Manu deposited an amount of Rs. 15000 in a bank which compounded, interest at the rate 6% annually. After two years, he deposited 5000 rupees, more. How much amount would he get after 3 years?, 4. Joseph took out a loan of 25000 rupees from a bank which charges 10%, interest compounded annually. After two years, he paid back 10000 rupees., To settle the loan how much should he pay at the end of one more year?, 5. The simple interest at 5% got for a certain amount after 2 years is, 500 rupees. If interest is compounded annually, what would be the, interest for same amount at the same rate after 2 years?, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Money Maths _ Worksheet 5.2, , Now try the following questions....., , 1. Raju deposited an amount of Rs. 20000 in a bank which compounded, interest at the rate 6 % annually. How much amount would he, get after 2 years?, 2. James took out a loan of 25000 rupees from a bank which charges 10%, interest compounded annually. To settle the loan how much should he, pay at the end of 3 years?, 3. Manseer deposited an amount of Rs. 15000 in a bank which compounded, interest at the rate 8% annually. After two years, he deposited 10000 rupees, more. How much amount would he get after one more year?, 4. Jewel took out a loan of 20000 rupees from a bank which charges 12%, interest compounded annually. After two years, she paid back 10000 rupees., To settle the loan how much should she pay at the end of 3 years?, 5. Akhil deposited 10000 rupees in a bank which pays 9% interest, compounded annually. How much would he get back after 3 years?, , Devapriya V Prabhu, TDHS, Mattancherry

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1, , Money Maths _ Worksheet 5.3, , STANDARD 8, , WORKSHEET 5.3, CHANGING TIMES, , Example, , Amount after one year = 12480 + 499.2, = 12979.2 Rupees, , Devapriya V Prabhu, TDHS, Mattancherry, , Look at the, Example....

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2, , Money Maths _ Worksheet 5.3, , Compound Interest Calculation, Annually, , Half Yearly, , Period of Time, , n, , 2xn, , Rate of Interest, , r%, , r, %, 2, , Amount, , P(1 +, , r, )n, 100, , P (1+, , (r /2) 2n, ), 100, , 1. Manu deposited an amount of Rs. 8000 in a bank which compounds, interest half yearly. The annual rate of interest is 6 %. How much, amount would he get after 1 year?, 2. A person took out a loan of 15000 rupees from a bank which charges, interest compounded half yearly. The annual rate is 10%. To settle, the loan how much should he pay at the end of 1 year?, 3. Varun deposited an amount of Rs. 20000 in a bank which compounded, interest every six months. The annual rate is 8%. After 1 year, he deposited, 10000 rupees more. How much amount would he get after one more year?, 4. Baby took out a loan of 25000 rupees from a bank which charges, interest compounded half yearly. The annual rate of interest is 12%., After 1 year, she paid back 10000 rupees. To settle the loan how, much should she pay at the end of 1 more year?, 5. Akhil deposited 10000 rupees in a bank which pays interest, compounded half yearly. The annual rate of interest is 12%., How much would he get back after 1 1 years?, 2, , *************, Devapriya V Prabhu, TDHS, Mattancherry

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2, , Money Maths _ Worksheet 5.4, , Compound Interest Calculation, Annually, , Half Yearly, , Quarterly, , Period of, Time, , n, , 2xn, , 4xn, , Rate of, Interest, , r%, , r, %, 2, , r, %, 4, , Amount, after n, years, , P( 1 +, , r, )n, 100, , P ( 1+, , (r /2) 2n, ), 100, , P(1+, , r /4 4n, ), 100, , Now try the following questions...., , 1. Anu deposited an amount of Rs. 15000 in a bank which, compounds interest quarterly. The annual rate of interest is 8%., How much amount would she get after 1 year?, 2. Arun took out a loan of 20000 rupees from a bank which charges, interest compounded quarterly. The annual rate is 12%. To settle, the loan how much should he pay at the end of 1 year?, 3. Sheeba deposited an amount of Rs. 10000 in a bank which, compounded interest every three months. The annual rate is 8%., After one year, she deposited 10000 rupees more. How much, amount would she get after one more year?, 4. Kiran deposited 15000 rupees in a bank which pays interest, compounded quarterly. The annual rate of interest is 6%., How much would he get back after 9 months?, , Devapriya V Prabhu, TDHS, Mattancherry

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3, , Money Maths _ Worksheet 5.4, , 5. Shaju deposited 15000 rupees in a bank which compounds interest, half yearly and Deepak deposited the same amount in another bank, which compounds interest quarterly. The annual rate of interest is, 10% at both the banks. How much more would Deepak get after, one year?, , **************, , Devapriya V Prabhu, TDHS, Mattancherry

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2, , Money Maths _ Worksheet 5.5, , Now try the following questions...., , 1. The population of a country increases by 2% every year., If the present population of the country is 3 crores, what will, be the population after 3 years?, 2. It is estimated that a company manufacturing mobile phones, increases production by 30% every year. In 2018 it made, about 8 crore phones. How many handsets does it expect to, produce in 2021?, 3. It is estimated that a company manufacturing washing machines, increases production by 5% every year. In 2019 it made, about 9 crore washing machines. How many washing machines, does it expect to produce in 2022?, 4. A TV manufacturer decreases the price of a particular model, by 6% each year. The current price of this model is 9000 rupees., What would be the price after 2 years?, 5. An air conditioner manufacturer decreases the price of a, particular model by 20% each year. The current price of this, model is 40000 rupees. What would be the price after 2 years?, , *************, , Devapriya V Prabhu, TDHS, Mattancherry