(d) Straight angle An angle whose measure is exactly 180° is called a straight angle.In the figure ∠AOB is a straight angle as it is 180°. ∠AOC + ∠COB = ∠AOB = 180°.(e) Reflex angleAn angle whose measure is more than 180° but less than 360° is called reflex angle.In the figure ∠AOB is a reflex angle as it is 240°.(f) Complete angleAn angle whose measure is exactly 360° is called a complete angle.In the figure a complete angle is shown.(g) Zero angleAn angle whose measure is 0°, is called zero angle. It has only one line segment.Classwork1. Using set square, classify the following angles:(a)NMO(b) MO N(c)Q RP(d)O A B(e) EO D(f)A BC2. Classify the following angles as acute, right, obtuse, straight and reflex angles:10°, 20°, 90°, 120°, 110°, 240°, 60°, 115°, 70°, 80°, 140°, 130°, 75°, 315°180°A O B A O B C 240°O B A 360°O A A B Acme Mathematics 6 251
3. Fill in the blanks:(a) The angle exactly 90° is called .....................(b) 60° is an ............... angle.(c) An angle grater than 90° is called .................(d) ∠AOB is .................. angle.Exercise 5.21. Match the following:O B A F G EO A O D CK O L A B A O B obtuse anglereflex angleright anglezero anglestraight anglecomplete angleacute angleA O BWow! Remember The definition252 Acme Mathematics 6
2. Measure the following angles using protractor:(a) (b) (c)(d) (e) (f)(g) (h) (i)3. Measures the following angles:(a) (b) (c)BO A O EDF GOO NMO RPSO TU OVX OYOZY∠AOB = ....................∠AOC = ....................ACOB∠AOC = ....................∠COB = ....................CA O B∠AOC = ....................∠BOC = ....................BOACAcme Mathematics 6 253
(d) (e) (f)4. Measure the marked angle in angular man given below:5. Study the figure given alongside and fill in the blanks.(a) ∠EOF is ........................................... angles.(b) ∠EOC and ∠COF are ...................... angles.(c) ∠AOD and ∠DOB are ..................... angles.(d) ∠COF is ............................................ angle.(e) ∠AOD and ∠COB are ...................... angles.(f) ∠AOB is ............................................ angle.(g) ∠AOD is ........................................... angle.6. Look at the given figures and write True or False in the boxes.(a) The value of 'y' is 10°. (b) The value of 'x' is 70°. (c) The value of 'b' is 60°. (d) The value of 'c' is 110°.(e) The sum of x° and 20° are straight angles. ∠AOD = ....................∠BOC = ....................ADOBC∠AOC = ....................∠BOD = ....................AO DBC∠AOD = ....................∠COB = .....................DOBACF C E O A D B 20° x° b° c° a° 70° 254 Acme Mathematics 6
(f) The sum of 70° and a° are right angles. (g) a° and 6° are equal. (h) y° is less than 170°. 7. Measure the following angles and write their types also.(a) (b) (c)(d) (e) (f)8. Draw the following angles using protector. (a) 48° (b) 63° (c) 135° (d) 205°(e) 225° (f) 300° (g) 360° (h) 0°9. Construct the angle whose measure is same as the angles given below:(a) (b) (c)(d) (e) (f)170° y O B A O B D X Z Y O P RA O B O X RO BAP QRXY ZAOBFEDODAAcme Mathematics 6 255
10. Calculate the value of ‘x’ when sum of x and given angles are right angle.(a) 44° (b) 35° (c) 80° (d) 10°(e) 25° (f) 63° (g) 70° (h) 89°11. Calculate the value of ‘y’ when sum of ‘y’ and given angles are straight angle. (a) 43° (b) 37° (c) 82° (d) 110°(e) 125° (f) 163° (g) 170° (h) 90°12. Find the value of 'x' in each case, when sum of angles is 90°.(a) (b) (c)(d) (e) (f)[Hint use sum of angles = 90°]13. Calculate the value of 'z' in each angle when sum of angles is 180°.(a) (b) (c)(d) (e) (f)30° x° x 2x30°(x – 1)° (x – 3)° x°(4x – 2)°2x° x° 2x°(x – 2)°(x – 2)°70°(2x – 1)°(x + 5)°50°30°z°30°z°z° z° z° z°(z + 1) 70°z°(z – 2)° (z – 2)°(z – 2)° 72°(10+z)°6z°256 Acme Mathematics 6
14. Calculate the value of x°, y°, z° in each case. (use straight angle)(a) (b) (c)(d) (e) (f)F. Construction of Angles Using Set SquareAngles can be construct using the set- squares. There are two triangular set - square in our geometry box. These are the set-squares.60°90°30°90°45°45°It is right-angled isosceles triangle It is right-angled scalene triangleWe can construct 30°, 60°, 45°, 90° and 75° using set-squares.(a) Construction of 30°.Given below is a scalene-set square. Choose 30°. Draw lines along OA and OB using pencil. Remove the set-square. ∠AOB = 30°80°100°y°x°Z°20° x°y° z°y°x°89°105°3z°x°y° 50°(x + 9)°z°y° 90°z°y°y°x°OAB OAB30°Acme Mathematics 6 257
(b) Construction of 60 °.Given below is a scalene-set square. Choose 60°. Draw lines along OA and OB using Pencil. Remove the set- square. ∠AOB = 60°(c) Construction of 45 °.Given below is a isosceles-set square. Choose 45°. Draw lines along OX and OY using Pencil. Remove the set- square. ∠XOY = 45°(d) Construction of 90°.Take any one of the set-square. Choose 90°. Draw lines along OA and OB. Remove the set-square. ∠AOB = 90°(e) Construction of 75 °.Choose 45°and 30°. Draw lines along OA and OB using Pencil. Remove the set-square. ∠AOB = 75°OAB O BA60°XO YXO Y45°O BAO BA90°O BAO BA75°258 Acme Mathematics 6
G. Construction of bisector of angleBisector is a line that divides a given angle into two equal angles.Let us bisect an angle of 60° Daw an angle of 60° using set-square.∠AOB = 60°. (fig i) Take O as foot of compass and take any arc cutting OA at P and OB at Q with compass. (fig ii) Put, foot of compass at P and draw an arc at D. (fig iii) Put, foot of compass at Q and draw an arc at D. (fig iii) Join the points O and D. (fig iv)Now, line OD is the bisector of ∠AOB.Where, ∠AOD = ∠DOB = 30°H. Construction of angles using compass and scale(a) Construction of 60° Draw a line, AB = 5 cm. Put the foot of the compass at A and take an arc which cut AB at C. Taking the same arc, put the foot of compass at C and cut the first arc at D. Join A and D and extend AD to O using scale.Now, ∠OAB = 60°.(b) Construction of 120° Draw a line, AB = 5 cm.Follow the steps of 60°, up to second and third steps.OPQAO BAB60°OPQABDOPQABD30°30°We can Bisect any angle following the above steps.A 5 cm B A C BADC B ADOC60° BA CDA 5 cm B B(i)(iii) (iv)(ii)Acme Mathematics 6 259
Taking the same arc, put foot of compass at D and cut the arc CD at E. Such that arc CD = arc DE. Join A and E and extend it to F.Now, ∠FAB = 120°(c) Construction of 90° Follow the steps of 120° up to second last step. Put foot of compass at E and draw the arc above the E. Taking a same arc put foot of compass at D and draw the arc above D which cut the first arc at F. Join A and F.Now, ∠FAB = 90°(d) Construction of 45° Draw an angle of 90°.∠FAB = 90°. Bisect the angle FAB. Now, ∠GAB = 45°, half of 90°. Similarly, we can construct the angle 30°, 135°. etc.Classwork1. Draw the following angles. Use protractor, scale and pencil:(a) 10° (b) 20° (c) 30° (d) 50° (e) 50°(f) 25° (g) 35° (h) 45° (i) 75° (j) 90°(k) 120° (l) 135° (m) 150° (n) 170° (o) 180°A CD EBF120° A CD EBA CE DBFAFCE D90° BAFGC45° A BFCE D90° B260 Acme Mathematics 6
Exercise 5.31. Construct the following angles using set-square.(a) 30° (b) 45° (c) 60° (c) 90°2. Construct the following angles using protector and bisect them.(a) 20° (b) 40° (c) 80° (d) 110°3. Construct the following angles using compass and scale.(a) 60° (b) 120° (c) 90° (d) 30°(e) 45° (f) 75° (g) 135° (h) 150°4. Construct the following angles in your copy and bisect them.(a) (b)(c) (d)(e) (f)AO B PO Q XO X DF O A O BRAMAcme Mathematics 6 261
5.2 Triangle and QuadrilateralA. Classification of triangle according to their sidesActivityMeasure the angles of the given triangle and complete the table:(a)AB BC CA Result(b)PQ QR RP Result(c)MN NO OM ResultNow Discuss about the nature of sides in every triangle.(a) Equilateral triangleA triangle in which all sides are equal is called an equilateral triangle. ∆ABC is an equilateral triangleas sides AB = BC = CA.(b) Isosceles triangleA triangle in which two sides are equal is called an isosceles triangle.∆ PQR is an isosceles triangle as its sides PQ = PR.(c) Scalene triangleA triangle in which no two sides are equal is called scalene triangle. ∆XYZ is a scalene triangle as XY ≠YZ ≠ ZX.B CAQ RPNOMB CAQ RPY ZX262 Acme Mathematics 6
B. Classification of triangle according to their anglesActivityMeasure the angles of the given triangle and complete the table:(a)∠YXZ ∠XYZ ∠YZX ResultAll angles are less than 90°.(b)∠BAC ∠ABC ∠BCA Result(c)∠EDF ∠DEF ∠EFD ResultNow, discuss the nature of the angles in every triangle.(a) Acute-angled triangleA triangle in which all angles are acute is called acute angled triangle.∆ABC is an acute angle triangle as its all anglesare less than 90°.(b) Right-angled triangleA triangle in which one angle is a right angle is called a right-angled triangle.∆ABC is a right angled triangle as its ∠ B is 90° (a right angle).(c) Obtuse - angled triangleA triangle in which one angle is obtuse is called an obtuse angled triangle.∆MNO is an obtuse angled triangle as ∠MNO is 120° (an obtuse angle).EFD50° 60°70°AB CAB CMN O120°Y ZXAB C90°Acme Mathematics 6 263
Classwork1. Fill in the blanks.(a) All sides of equilateral triangle are ........................ .(b) Two sides are equal in ........................ triangle.(c) No sides are ........................ in scalene triangle.(d) All angles are equal in ........................ triangle.(e) One angle is ........................ in right angle triangle.(f) One angle is more than 90° in ........................ triangle.2. Tick () the right statements.(a) There are 3 acute angles in right angled triangle.(b) Two angles are right angle in obtuse angled triangle.(c) Obtuse angle is not possible in acute angled triangle.(d) Two obtuse angles are possible in a triangle.(e) All three sides are equal in equilateral triangles.(f) There are 4 type of triangles according to their sides.(g) There are 3 type of triangles according to their angles.Exercise 5.41. Classify the following triangles according to their sides:(a) (b) (c)A2 cm3 cmB 4 cm CDE F4.5 cm4.5 cmY 4 cm Z4 cm4 cmX264 Acme Mathematics 6
(d) (e) (f)(g) (h)2. Match the following.Isosceles triangleScalene triangleAcute-angled triangleEquilateral triangleRight-angled triangleObtuse-angle triangle40° 80°60°120°4 cm4 cm2 cm Y 3 cm Z3 cm3 cmX4 cm2.5 cm5 cm3.5 cm3.5 cm3.5 cm2 cm3 cm3 cmAcme Mathematics 6 265
3. Classify the following triangle according to their angles:(a) (b) (c)(d) (e) (f)4. Measure the angle of the given triangle and find their sum:(a) (b) (c)(d) (e) (f)5. Classify the following triangles according to their sides. (Measure the sides)(a) (b) (c)6. Classify the following triangles according to their angles. (Measure the angles)(a) (b) (c)80°40°60° 90° 40°50°130°30° 20°70° 30°80°55° 85°40°30°60°90°AB CDE FGH IP RQXYZ OMNA CBQ R P DE FB CA Q RP N OM 266 Acme Mathematics 6
7. Construct a triangle ABC, where ∠ABC = 70°.(a) Write the measure of angle A.(b) Write the measure of angle B.(c) Write the length of side AB, BC and CA.(d) Write the type of triangle.8. Construct a triangle ABC, where ∠B = 60° and ∠C = 60°(a) Write the measure of angle A.(b) Write the measure of sides AB, BC and CA.(c) Write the type of triangle.E Quadrilateral A quadrilateral is a closed figure bounded by four sides. In the figure ABCD is a quadrilateral. AB, BC, CD and AD are four sides.∠A, ∠B, ∠C and ∠D are its 4 angles.Here are some special quadrilaterals.(a) RectangleABCD is a rectangle. Its all angles are right angles. Its opposite sides are equal. AD = BC and AB = DC Its opposite sides are parallel. AD||BC and AB||DC.(b) SquarePQRS ia a square. Its all angles are right angles. Its opposite sides are parallel. Its all sides are equal.(c) ParallelogramABCD is a parallelogram. Its opposite sides are parallel. Its opposite sides are equal.AD C B ADB C PS R Q A BD CAcme Mathematics 6 267
(d) Rhombus ABCD is a rhombus. Its all sides are equal. AB = BC = CD = DA Its opposite sides are parallel. AB||DC and BC||AD. Its opposite angles are equal ∠A = ∠C and ∠B = ∠D Its diagonals are not equal. diagonals AC ≠ diagonal BD. Its diagonals bisect each other at 90°. AO = OC and BO = OD. AC ⊥ BD. Diagonals of a rhombus bisect the angle at the vertex.(e) Trapezium If a quadrilateral has a pair of opposite sides parallel then it is called trapezium. ABCD is a trapezium. Its two sides AD and BC are parallel. Classwork1. Fill in the blanks.(a) All sides of quadrilateral are equal in ........................ .(b) Four sides are equal in ........................ quadrilateral.(c) No sides are equal in ........................ .(d) All angles are equal in ........................ .(e) All angle are right angle in ........................ .(f) Only two sides are parallel in ........................ .2. Tick () the right statements.(a) There are 4 acute angles in a quadrilateral.(b) Two angles are right angle in trapezium.(c) Reflex angle is not possible in a quadrilateral.(d) Opposite sides are equal in rectangle.BACDBACO90°DB CA D268 Acme Mathematics 6
(e) All side are equal in parallelogram.(f) There are 4 type of quadrilaterals according to their sides.(g) There are 3 type of quadrilaterals according to their angles.Exercise 5.51. Find the size of angles of the given quadrilateral (use protractor):(a) (b) (c)(d) DABC(e) (f)SPQR2. Measure the length of sides of the following quadrilaterals.(a) (b) (c)(d) (e) (f)CBAD S RP QD OMNAB CDQPRSACDBKNMLGH EFWX YZA BD CAcme Mathematics 6 269
3. Measure the angles and sides of the given quadrilateral and write the conclusion.(a)∠ABC = AB =∠BCD = BC =∠CDA = CD = ∠DAB = DA = Result All angles and sides are different in size. So it is a quadrilateral only.(b)∠PQR = PQ =∠QRS = QR =∠RSP = RS =∠SPQ = SP =Result(c)∠MNO = MN =∠NOP = NO =∠OPM = OP =∠PMN = PM =Result(d)∠BCD = BC =∠CDE = CD =∠DEB = DE =∠EBC = EB =ResultD CBAP SQ RM PN OBE DC270 Acme Mathematics 6
(e)∠ADC = AD =∠DCB = DC =∠CBA = CB =∠BAD = BA =Result(f)∠GDE = GD =∠DEF = DE =∠EFG = EF =∠FGD = FG =Result4. Measure the angles of the given quadrilateral and fill in the table.(a) (b) Fig ∠A ∠B ∠C ∠D ∠A + ∠B + ∠C + ∠D(a)(b)(i) Are ∠A, ∠B, ∠C and ∠D equal in both quadrilateral ?A DB CGDEFA BCDADBCAcme Mathematics 6 271
(ii) Are sum of angles equal in both quadrilaterals?5. Find the value of x or y in the following quadrilaterals:(a) (b) (c )(d) (e) (f)Dx65°75°68°CA BPQS95°80° 80°xREDB y25°20°260°C110° 115°80°A DyBC120°80°DCA B E100°y 100°Q 90°PSR80°x1. Objective : To make different shapes of quadrilateral.2. Materials required: Tangram Scissors Glue A4 sized paper3. Activity:a. Make tangram and level the 7 pieces.b. Choose the pieces and construct quadrilaterals.1 237564It is a square.10 cm10 cm64Project Work272 Acme Mathematics 6
G CircleActivityLook, discuss and learn.1. What is the name of the given shape?2. Are these figures enclosed by straight line?3. Are OA and OB equals?4. What is the name of line AB called?5. Where are the paints A, B, C and D?6. Where is the point O?The figure given above is a circle.A circle is a closed figure. Circle is not bounded by straight lines. It is bounded by curved line. Points A, B and C are on the curved line. O is the point equidistant from the points A, B and C. O is called the 'centre' of the circle. OA is called the 'radius' of the circle. XY is the line segment through centre of the circle O. It is called the 'diameter'. The diameter of a circle is twice its radius. (a) Chord of a circleXY and AB are the chords of the circle. We can draw large number of chords. Diameter is the longest chord. (b) Arc of a circleThe part of the circle is called the arc of the circle. AB is the arc of the given circle. BD CA OX YOC AOBA BOABOAcme Mathematics 6 273
(b) Circumference and semicircleHalf of a circle is called a semicircle. ABC is a semicircle. Similarly, ADC is also a semicircle.Sum of ABC and ADC is a full circle.The length around the circle is called circumference.Circumference of a circle is called the perimeter of the circle.(c) SectorThe shaded part is the sector of the circle. It is the area between the two radii.Exercise 5.61. Name the parts of the given circle. 2. Name the chords. 3. Find the diameter of the circle whose radius is given below. (a) 2 cm (b) 3.5 cm (c) 4 cm (d) 5 cm 4. Find the radius of the circle whose diameter is given below. (a) 8 cm (b) 6.6 cm (c) 70 cm (d) 7 cm 5. Fill in the blanks. (a) A diameter is the ............. chord of a circle. (b) Perimeter of a circle is called the .......... of the circle. (c) A ............ divides the circle into two semicircles.ADBCOA COBBCAOADCBOQ. No. 1 Q. No. 2274 Acme Mathematics 6
5.3 SolidsA. IntroductionLook at the following figures carefully.(a) (b) (c)(d) (e) (f)The above figures are the figures of the solids. A solid has length, breadth and height. Some solids are given below.Solid Name ExampleSphereCuboidCubeCylinderLength (l) breadth (b) height (h)Acme Mathematics 6 275
ConePyramid(a) Cylinder Cylinder is a solid shape. It has 2 circles at the two ends and curved surface. It has no vertices. Drum, gas cylinder, Juice can are examples of cylinder. (b) Cone Cone is a solid shape. Its base is circular in shape and the surface is curved. Its curved surface meets at a point. It has a vertex.The examples of cone are given below. Ice-cream Funnel Road Divider vertexbasecurved surface276 Acme Mathematics 6
(c) SphereA sphere is a solid bounded by one surface, which is such that all points on its surface are equidistant from a fixed point (lying inside the solid). The fixed point is called the centre and the fixed length that joins the centre to any point on the circumference is called the radius of the sphere. HemisphereWhen a sphere is exactly divided into two equal parts by cutting the sphere along the diameter then each part is called a Hemisphere.B CubeA cube is the most common solid shape.Dice is a cube. It has six faces. All faces are equal and rectangular. All faces are square in shape.Six faces of dice are given below:Net of the cubeIt is a net of the cube. It has 6 squares. If we fold up it changes into a cube.Skeleton of a cubeIn the figure alongside Fig. (ii) is the skeleton of fig (i). It is made from the ‘juice’ pipe and thread. A, B, C, D, E, F, G and H are its vertices. AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG and DH are its edges.Dimensions0 1 2 3fig. (i)It is solidE HG FDB CAfig. (ii)1 3 6 4251 2 3 4 5 6Acme Mathematics 6 277
There are 8 vertices and 12 edges. In the figure, number of pieces of juice pipe arethe edges of solid.The cube has: 6 surfaces 8 vertices 12 EdgesC CuboidA cuboid is also a common solid shape. Brick is a cuboid. It has six faces. All faces are not equal. Opposite faces are equal. All faces are rectangular in shape.Six faces of brick are given below:Net of the cuboid 1 2 3 4565 2 6143It is a net of the cuboid. It has 6 rectangles. If we fold up it changes into a cuboid.Skeleton of a cuboidIn the figure alongside Fig. (ii) is the skeleton of fig (i). It is made from the ‘juice’ pipe and thread.SurfaceEdgeVertexfig. (i)It is solid278 Acme Mathematics 6
A, B, C, D, E, F, G and H are its vertices. AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG and DH are its edges. There are 8 vertices and 12 edges. In the figure, number of pieces of juice pipe arethe edges of solid.The cuboid has also 6 surfaces, 8 vertices and 12 Edges.D Parts of the solid shape(i) Face: Face is the surface of a solid.(ii) Edge: Edge is a straight line where two faces meet.(iii) Vertex: Vertex is a point where three or more than three edges meet.1. Relation between faces, edges and vertices:Let's count the number of faces, edges and vertices of the following solids and complete the table.Cube Cuboid PyramidSolidsNumber of faces (F)Number of verticals (V)Number of edges (E)F + V – ECube 6 8 12 6 + 8 – 12 = 2Cuboid .......................... .......................... .......................... ..........................Pyramid .......................... .......................... .......................... .......................... Hence, F + V – E = 2 E HF GDB CAfig. (ii)It is face.It is edge.It is vertex.F + V – E = 2It is Euler's formula.Acme Mathematics 6 279
E Construction of some models of the solidsNet of solids: A net is a pattern that can be cut and folded to form a solid shape. Some solids and their nets are given below.SN Name Solid Figure Net Figure1 Cuboid2 Cube3 Pyramid4 Cylinder5 Cone1. Circle the correct word that describe each shape.sphere prism cone cylinderClasswork280 Acme Mathematics 6
3. Fill in the blanks.(a) Number of vertices of a cube are ....................... .(b) There are ....................... faces on the cylinder.(c) A cone has ....................... vertex.(d) ....................... has 12 edges.(e) Sphere has ....................... surfaces.(f) ....................... has one vertex.(g) ....................... has no vertices.(h) Cuboid has ....................... parallel lines.2. Write the number of surfaces, vertices and edges of each figure:Eraser : cuboidNo. of Vertex : .............No. of Faces : .............No. of edges : .............No. of Vertex : .............No. of Faces : .............No. of edges : .............No. of Vertex : .............No. of Faces : .............No. of edges : .............cone sphere cylinder prismsphere cone pyramid cubesphere cuboid pyramid cylindercube sphere cone pyramidAcme Mathematics 6 281
Exercise 5.71. Name the following solid figures.(a) (b) (c)(d) (e) (f)2. Name the solid that the following net represents.(a) (b) (c)(d) (e) (f)3. Tick () the correct net that will form cuboid:(a) (b)282 Acme Mathematics 6
4. Write the number of surfaces, vertices and edges of each figure and verify Eular’sformula.(a) (b) (c)(d) (e) (f)5. Fill in the blanks.(a) ………. shapes have edges, vertices and faces.(b) Vertex is the point where two ………. of a solid meet. (c) Cuboid has ………. faces.(d) Cube has ………. vertices and ………. edges.6. A toothpaste box has 6 faces and 8 corners.(a) Find the number of edges. (b) Find F – F.(c) Is V – E + F = 2 true for toothpaste box.7. Define the followings.(a) Cube (b) Corners (c) Faces (d) Cuboid8. Write any two difference between cuboid and cube.9. The box has 12 edges and 8 corners. Find the its number of faces.10. Study the given figure:(a) Name the figure. (b) How many vertices does it has?(c) How many surfaces does it has?(d) How many circles does it has?11. Draw the followings solids.(a) Cone (b) Sphere (c) Cylinder (d) Cuboid12. What is difference between plane figure and solid figure.Collect different solid shapes around you and paste the pictures in A-4 paper and present in the class.Project WorkAcme Mathematics 6 283
1. (a) Name the figure.(i) (ii)(b) Write the types of an angleIt is a .................................. angles.(c) Construct a line segment, AB = 4 cm and draw its perpendicular bisector.(d) Fill in the blanks.(i) Equilateral triangle has ............................. sides equal.(ii) Acute angled triangle has ………………. angles acute. 2. (a) Fill in the blanks.(i) These lines are ....................... lines.(ii) These lines are ....................... lines.(b) Write the types of an angle.It is a .................................. angles.(c) Construct an angle of 75° using compass.(d) Fill in the blanks.(i) Quadrilateral has ………………. sides.(ii) Rhombus has ………………… sides.70°Mixed Exercise284 Acme Mathematics 6
3. (a) Fill in the blanks.(i) These lines are ....................... lines.(ii) These lines are ....................... lines.(b) Define reflex angle.(c) Calculate the value of x, y and z from the given figure.(d) Fill in the blanks.(i) Obtuse angled triangle has ………………. angles acute. (i) Square has ………………. sides equal.4. (a) Construct a pair of intersecting lines.(b) Construct an angle of 40° using protector.(c) Draw the net of cuboid.(d) Name the figures.(i) (ii).............................. .............................5. (a) Construct an angle of 60° using protector.(b) Define scalene triangle.(c) Taking a cuboid, verify the “Euler’s formula”.(d) Find the value of x°. from the given figure.6. (a) Define square.(b) Calculate the value of ‘a’from the adjoining figure.y° 78°x° z°B CA D70°x°60°aA BD CAcme Mathematics 6 285
(c) Draw the net of cube.(d) Construct an angle of 120° using compass.7. (a) Name the solids.(i) (ii).............................. .............................(b) The vertices of a cuboid is supposed to be V, side is E and surface is F, then which of the following is the relation between them? Write it.(i) V + E + F = 2 (ii) V - E + F = 2(iii) V + E – F = 2 (iv) V – E – F = 2 (c) Calculate the value of ‘x’ from the given quadrilateral.(d) Name the figures.(i) (ii)8. (a) The vertices of a cube is supposed to be V, side is E and surface is F, then write the relation between them. (b) Fill in the blanks. The line joining the two points on the circumference and through centre of the circle is called ...........(c) By using ruler, draw a line segment AB = 6 cm. By using compass construct ∠XAB = 80° at A. (d) What type of triangle is formed by joining the points X,Aand B? Give reason.89°x°80°100°A BCDP QS R286 Acme Mathematics 6
9. (a) In the given figure, write the relation betweenAB and CD as well as CD and EF.(b) By using a protractor measure the angles and measure all sides using scale of the given quadrilateral. On the basis of measure what type of quadrilateral is this? Write it.10. (a) Fill in the blanks.(i) The line joining the two points on the circumference of the circle pass through the center is know as ......................... .(ii) The formula to find the perimeter of rectangle is ..................... .(b) (i) By using ruler, draw a line segment QR = 6 cm. By using compass construct ∠PQR = 90° at Q.(ii) What type of triangle is formed by joining the points P, Q and R? Givereason.11. (a) Find the value of ‘x’ and ‘a’.(b) By using a protractor, measure the angles of the given triangle. On the basis of angles what type of triangles is this?Write it.12. (a) Tick () the correct answer. AB and CD are ............. lines.(i) Parallel(ii) Perpendicular(iii) Intersecting(b) Two lines intersecting each other with 90° are called .................. lines.(c) Draw a line segment of length 8 cm and perpendicularly bisect it.ABEFDCA BD Cx 50°aABOCD AB CACBDAcme Mathematics 6 287
13. (a) How many types of angles are there?(b) Angle less than 90° is called ........................... angle.(c) Construct an angle 60° using protractor and bisect it using compass.14. (a) Find the value of x from the given figure. 80° x(b) Construct angle 45° using compass.15. (a) Define acute and right angle with examples.(b) Draw an angle 90° by using compass.(c) Define equilateral triangle.16. (a) Find the value of x. 45°x(b) Find the value of x based on the figure given below when ∠AOB is a straight angle.5x + 20° 75°A BCO17. (a) In the given figure, write down the relationship between:(i) PQ and AB(ii) PQ and RS(b) Draw a line segment of 6.8 cm and draw the perpendicular bisector of it.18. From the triangle PQR given along side, answer the following questions.(a) What type of triangle is ∆PQR? Give reason.(b) Name two equal sides of ∆PQR.(c) What is the relation between ∠QPR and ∠PQR?A Q S BP RP Q55°R288 Acme Mathematics 6
1. Objective : To Construct Different Polygons.2. Materials required: 40 rectangular strips of different size with width 12 cm. Colours Gum.3. Activity:(a) Colour the stirps 10 red, 10 black, 10 green and 10 yellow.(b) Paste the strips of different colours to make different polygon on A4 paper.4. Conclusion(a) Haw many strips you used to make different polygon ?(b) What shapes are farmed using same sized strips ? (c) What shapes are farmed using different size strips ? (d) Which shape required the least number of strips ?5. An example is given below: It is equilateral triangle. It has 3 strips. All are same size strips.Project WorkAcme Mathematics 6 289
1. Objective : To verify the Sum of angles of a quadrilateral is 360°.2. Materials required :Sheet of paper, Colours, Gum, Scale and Scissors3. Activity: Draw a quadrilateral on the paper. Mark the four angles 1, 2, 3 and 4 as shown in the figure. Cut out the quadrilateral Colour the angle 1 red. Colour the angle 2 yellow. Colour the angle 3 green. Colour the angle 4 blue. Tear off (cut) each angle as shown. Stick the 4 angles in your copy like this. (given alongside.)4. What do you observe?4 angles made a complete turn or 2 straight angles.So, ∠1 + ∠2 + ∠3 + ∠4 = 360°.Hence, sum of angles of a quadrilateral, is 360°.1 23 414 321 23 41 23 4Project Work290 Acme Mathematics 6
1. Objective : To classify the triangles according to their sides.2. Materials required :A-4 size paper, Scale, A pair of scissors, Glue, Different colours3. Activity: Cut the paper in triangular shape Colour each shape with different colours. Stick (paste) each triangle on A-4 size paper Measure each sides of triangles. Classify the triangles according to their sides.4. Example:Observation:Is there any equilateral triangles? If yes, you are lucky.Project WorkAcme Mathematics 6 291
1. Objective : To make skeleton model of different shapes.2. Materials required: Juice pipe 100 pcs. Thread a role. Long needle 1 pcs. A pair of scissors.3. Activity:Example:Here are some nets. Use these nets to make the skeleton models.(a) (b) Tetrahedron Pyramid(c) (d)Triangular prism OctahedronThe shape you made is called the skeleton models.Project Work292 Acme Mathematics 6
EvaluationTime: 67 minutes Full Marks: 281. (a) (i) The line segment joining the centre and circumference of a circle is called ............ [1](ii) The vertices of a cube or cuboid is supposed to be V, side is E and surface is F, then write the relationship between them. [1] (b) By using rular draw a line segment BC=7cm. By using compass, construct ∡ABC = 90° at B. [3](c) There are 6 faces, 12 edges in the chalk box. Find the number of vertices. [1]2. (a) How many types of angles are there ? [1](b) Angle less than 90° is called ................ angle. [1] (c) Draw a triangle MKL with MKL = 120°.Find the measures of the remaining angles using the protractor. [3]3. (a) Choose the correct option.PQ and RS are ............ lines. [1](i) Intersecting (ii) Parallel (iii) Perpendicular (b) Classify the given angle in to acute, right, obtuse and reflex angle. [1] 205o, 120o, 35o, 90o (c) Draw a line segment of length 7.4cm andperpendicularly bisect it. [3] (d) Given the geometry figure. Write measurement of the diameter. [1]4. (a) Define parallelogram. [1](b) Draw the 120° angle using the compass and ruler. [3](c) In an equilateral triangle, all angles are .................degree. [1] (d) Classify the given triangle on the basis of its side. [3](e) Classify the given quadrilateral bymeasuring their sides and angles. [3]PQSRP R OAB CDPQ RAcme Mathematics 6 293
Warm Up Test1. Study the given graph and try to answer the following questions.(a) How far is the point A from the starting point 0?(b) Which point is represented by (3, 3)? (c) Is point C represented by (6, 2)?(d) If D (2,5) is given2 presents ................................5 presents ................................2. Study the graph alongside and write;(a) The co-ordinates of A(b) The co-ordinates of B(c) The co-ordinates of CA Co-ordinate axisIn the figure two straight lines OX and OY are intersecting at O perpendicularly. OX is horizontal number line and OY is vertical number line.OX is called the X-axis.OY is called the Y-axis.Now, YOX is a plane. O is called origin. In this plane we define the position of the object as a point.B Co-ordinatesA system which describes the position as a point was invented by a French mathematician Rene Descartes in the 17th century. He describe point A as (2, 3) and said that 2 units to the right from the origin and 3 units up from the x-axis (OX).ABCC0 112345672 3 4 5 6 7ACB0 112345672 3 4 5 6 711223344556677OXY5.4 Co-ordinate294 Acme Mathematics 6
A(2, 3)O XY1123452 3 4 5Y-coordinates is also called the ordinates.X-coordinates is also called the abscissa.In the above figure A (2, 3) is a point. Where 2 represent the value of 'x' and 3 represent the value of 'y'. We always write x-coordinate at the first and y-coordinate in the second as(2, 3). (2, 3) is called the coordinates of the point A. (2, 3) is also called the order pairs.C QuadrantsIf we include the negative numbers in the number line OX and OY then we get the XX' as x-axis and YY' as y-axis.Now, XOX' and YOY' divides the plane into four equal parts, called Quadrants.XOY is called first quadrants. X'OY is called second quadrants. X'OY' is called third quadrants.XOY' is called fourth quadrants.D Sign in the quadrantsQuadrant x- coordinates y- coordinatesFirst + ve + veSecond – ve + veThird – ve – veFourth + ve – veE Plotting the pointsConsider the points A( 2, 3), B(– 3, 4), C(– 5, – 6) and D(3, – 4). A( 2, 3) is a point.Here, x-coordinate, 2 is + ve and y-coordinate, 3 is + veSo it is plotted on the 1st quadrant as 2 unit right and 3 units up.B (– 3, 4) is another point.Here, x-coordinate 3, is – ve and y-coordinate 4, is + veOY'X' XYOh! In X'OY plane, 'x' represent negative (–ve) part.Acme Mathematics 6 295
So it is plotted on the 2nd quadrant as 3 unit left and 4 units up. Similarly, C (– 5 , – 6) is plotted on 3rd quadrant and D ( 3, – 4) is plotted on 4th quadrant. The graph of the points A, B, C and D is given below.OY'X' XYD(3, – 4)A(2, 3)B(– 3, 4)C(– 5, – 6)Classwork1. Study the graph alongside and fill in the blanks.(a) x -coordinate of A = .......................(b) y- coordinate of P = ....................... (c) coordinate of Q = (6, ..........)(d) coordinate of K = (........., 4)(e) Two points with y coordinates 5 are ..............(f) Two points with x coordinates 6 are .............. (g) coordinate of B = (......., ........) and C = (..........., .................)2. Complete the followings:(a) If Q (– 6, 2) is a point, then its x- coordinate is ........ and y-coordinate is ..........(b) Coordinates of a point 4 units left and 2 units up is written as .......................(c) Coordinates of a point 6 units down from the origin is written as ........................(d) Coordinates of a point 6 units left from the origin is written as ...............................OABC PKQ11234562 3 4 5 6 7YX' XY'296 Acme Mathematics 6
3. From the graph along side write the coordinates.Coordinates of A = (..........., ..............)Coordinates of B = (..........., ................)Coordinates of C = (..........., ..............)Coordinates of D = (..........., .............)Exercise 5.81. Name the following lines:XX' = ............................YY' = ............................2. Fill in the blank.Coordinate of the origin is ...............................3. Write the coordinates of the points A and B.OXYAB4. Plot the following points on the graph.A (3, 4), B (7, 2), C(– 2, 6), D (– 7, 4)5. Plot the following points on the graph. (– 3, – 4), B (– 7, – 2), C (2, – 6), D (7, – 4)6. Write any four points along x-axis only. 7. Write any four points along y-axis only.OY'X' XYCDABY'X O X'YAcme Mathematics 6 297
8. Study the given graph and write the coordinates of the following points.OY'X' XYKA DBCFLJIHGE(a) A (b) B and C(c) D, E and F (d) G, H, I ,J, K and L9. On a square paper (graph paper), plot the following points and join them in order.(a) A (2, 3) and B (5, 6), join the line segment AB.(b) A (2, 3), B (– 2, 0) and C (2, 0), join the points and make triangle ABC.(c) A (– 3, 3), B (– 6, 2), C (–7, –2) and D (– 4,– 1), and join the points A, B, C, D and A.(d) A (5, 1), B (5, – 3), C (7, – 3) and D (7, 1), join the points A, B, C, D and A.10. Plot the points P (3, 5), Q (2, – 2), R (6, 0), S (6, – 3) on the graph and join the points in the order, make a closed figure. Name the figure.11. Draw a square on the graph and name it and colour it also.12. Plot the co-ordinates of the given points A(2, 3), B(6, 3), C(6, – 3) and D(2, – 3) in a graph paper. Join the points in order and write the name of the figure so formed. Also find its area.298 Acme Mathematics 6
5.5 Symmetry and TessellationsA. SymmetryLook at the following figures.Object Dividing into two equal parts Two identical partsmmmEach of the figure have equal half.These figures are called symmetrical figures.The line which divides the figures into two halves is called axis of symmetry. The axis of symmetry is like a mirror line. In the above figure line 'm' is a line of symmetry.Many of the letters of the English alphabet are also symmetrical.A B C E HAcme Mathematics 6 299
Figure having one line of Symmetry:l1 l1 l1Heart Butterfly Isosceles triangleFigures having two lines of Symmetry:l2l1Cross symboll2l1Rectanglel1l2Letter HFigure having three lines of Symmetry: Figures having four lines of Symmetry:l1l2l3Equilateral trianglel4l2l3l1SquareFigure having infinite lines of Symmetry: Figures having no line of Symmetry:l1l2l3l5l6 Parallelogram Scalene triangleClasswork1. Draw the following shapes and show all possible lines of symmetry.(a) Square (b) Rectangle (c) Equilateral triangle(d) Kite (e) Regular hexagon (f) Regular pentagon(g) Regular octagon (h) Isosceles trapezium (i) Isosceles triangle300 Acme Mathematics 6