1. Prepared By: Norisah Bt Mustaffa KOSPINT P O L Y G 0 N S T O P I C 1 0

3. Polygons A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines. three sided shapes 10.1 Recognizing Polygons

4. A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines. four sided shapes Recognising Polygons Polygons

5. A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines. five sided shapes Recognising Polygons Polygons

6. A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines. Recognising Polygons Polygons six sided shapes

7. A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines. seven sided shapes Recognising Polygons Polygons

8. Recognising Polygons Now you know what polygons are. Can you sketch eight sided shapes polygon? Do you know what the different types of polygons are called? Polygons

9. Are these shapes polygons? Recognising Polygons Polygons

10. Polygons These shapes are not polygons. They have no straight lines and are not closed diagrams. Recognising Polygons Not straight lines. Not all sides have straight lines. Not closed diagrams

11. Polygons Naming Polygons We name polygons according to the number of sides the polygons have. Look at the table below. Pentagon Quadrilateral Triangle Name Polygon Octagon Heptagon Hexagon Name Polygon

12. Polygons Sides of Polygons Side Side is a line which is part of a polygon

13. Polygons Vertices of Polygons Vertex The vertex of a polygon is the meeting point of two sides.

14. Polygons Diagonals of Polygons Diagonals A diagonal is a straight line that joins two non-adjacent vertices. How many diagonals in a quadrilateral?

15. Polygons To Find The Number of Diagonals in a Polygon A pentagon has 5 diagonals 1 3 2 2 diagonals can be formed 2 diagonals can be formed 1 diagonal can be formed

16. Polygons To Find The Number of Diagonals In A Polygon An octagon has 20 diagonals 1 2 3 4 5 diagonals can be formed 5 diagonals can be formed 4 diagonals can be formed 3 diagonals can be formed 2 diagonals can be formed 1 diagonal can be formed 6 5

17. Sketching Polygons Polygons We have to know the number of sides or vertices that the polygon has, to sketch a polygon. Label the polygon drawn by using the capital letters to name the vertices. 1) Sketch a triangle on dotted grids. Name the vertices of this polygon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A B C Are the number of sides and the number of vertices of a polygon are the same?

18. Polygons A shape has symmetry if it can be divided equally. So, that one half fit exactly onto the other. This shape is called symmetrical shape. 10.2 Symmetry: Determine and Drawing Lines of symmetry (2 lines of symmetry)

19. Polygons A shape has symmetry if it can be divided equally. So, that one half fit exactly onto the other. This shape is called symmetrical shape. Symmetry: Determining and Drawing Line of symmetry (One line of symmetry

20. Polygons A shape has symmetry if it can be divided equally. So, that one half fit exactly onto the other. This shape is called symmetrical shape. Symmetry: Determine and Drawing No line of symmetry. Shapes which are not symmetrical are called asymmetrical shapes

21. Polygons A symmetrical shape has a line or lines symmetry. When the shape is folded along the line of symmetry, one part of the shape overlaps exactly onto the other part. Symmetry: Determine and Drawing Can you determine the symmetry shape on the diagrams below?

22. Polygons Completing Symmetrical Shapes We can complete the shape when part of a symmetrical shape and the line (s) of symmetry are given.

23. Polygons 10.3 TRIANGLES A triangle can be drawn by using a protractor and ruler when, (a) the lengths of all the sides are given. (b) two angles and a side are given (c) two sides and an angle are given. C (b) 3cm 50 º 50 º P Q R 50 º K (c) 70 º 4cm 7cm J L (a) 5cm 4cm 6cm A B

24. Polygons Drawing Triangles Solution: Step 1: Make a sketch of ABC 60 ° 60 ° A B C 6cm Example: Draw a triangle with the given measurements. AB=6cm, A=60°, B=60°

25. Polygons Drawing Triangles Step 2: Draw AB=6cm using a pencil and a ruler. A B 6cm

26. Polygons Drawing Triangles A B 60 ° 6cm 165 ° 150 ° 135 ° 120 ° 105 ° 90 ° 75 ° 15 ° 30 ° 45 ° 60 ° 0 ° 180 ° 180 ° 165 ° 150 ° 135 ° 120 ° 105 ° 75 ° 60 ° 45 ° 30 ° 15 ° 90 ° 0 ° Step 3: Use a protractor to draw A = 60 °

27. Polygons Drawing Triangles A B 60 ° 6cm 165 ° 150 ° 135 ° 120 ° 105 ° 90 ° 75 ° 15 ° 30 ° 45 ° 60 ° 0 ° 180 ° 180 ° 165 ° 150 ° 135 ° 120 ° 105 ° 75 ° 60 ° 45 ° 30 ° 15 ° 90 ° 0 ° 60 ° Step 4: Use a protractor to draw B = 60 °

28. Polygons Drawing Triangles Step 5: Point C is a intersection of the two lines drawn. A B 60 ° C 6 cm 60 °

29. Polygons Symmetry of Triangles Triangles with sides of different lengths has different number of lines of symmetry.

30. Polygons Geometric Properties of Different Types of Triangles Triangles are named based on their geometric properties. We can classify triangles into three types based on the length of their sides. Scalene Triangle All sides are of different length. Isosceles Triangle Two of its sides are of equal length. Equilateral Triangle All sides are of equal length

31. Polygons Geometric Properties of Different Types of Triangles Triangles also can be classified based on the size of the angles of the triangles. Acute Triangle All the angles are acute angles. Right Angled Triangle One of its angle is a right angle. Obtuse Triangle One of its angle is an obtuse angle.

32. Polygons Solving Problems Involving Triangles The sum of the angles of a triangle is 180°. a + b + c = 180 ° a = b = c = 60° p + q + r = 180 ° q = 90° p + r = 90 ° x + y+ z = 180 ° x = y a b c p q r x y z

33. Polygons Solving Problems Involving Triangles In the figure below, find the value of x. 48 ° x R P Q S Solution: Q= P=48° (Isosceles triangle) S = 90° The sum of the angles of a triangle is 180°. So, x = 180° - 90° - 48° = 42°

34. Polygons 10.4 QUADRILATERALS Quadrilaterals are polygons with four sides. A quadrilateral has four vertices and two diagonals.

35. Polygons QUADRILATERALS Determining and Drawing Lines of Symmetry of Quadrilaterals side diagonals line of symmetry vertex

36. Polygons QUADRILATERALS Determining and Drawing Lines of Symmetry of Quadrilaterals 4 lines of symmetry 2 lines of symmetry no line of symmetry

37. Polygons Drawing Quadrilateral Quadrilateral can drawn using a ruler and a protractor when three sides and two angles are given. Example: Draw ABCD below to scale using a ruler and protractor. A B D C 6 cm 3 cm

38. Polygons Drawing Quadrilateral Step 1: Draw a 6 cm line using a ruler and pencil. Name the line AB A B 6 cm

39. Polygons Drawing Quadrilateral Step 2: Use a protractor to draw perpendicular lines from points A and B. A B 6 cm 165 ° 150 ° 135 ° 120 ° 105 ° 90 ° 75 ° 15 ° 30 ° 45 ° 60 ° 0 ° 180 ° 180 ° 165 ° 150 ° 135 ° 120 ° 105 ° 75 ° 60 ° 45 ° 30 ° 15 ° 90 ° 0 °

40. Polygons Drawing Quadrilateral Step 3: Use a protractor to draw perpendicular lines from points A and B A B 6 cm 165 ° 150 ° 135 ° 120 ° 105 ° 90 ° 75 ° 15 ° 30 ° 45 ° 60 ° 0 ° 180 ° 180 ° 165 ° 150 ° 135 ° 120 ° 105 ° 75 ° 60 ° 45 ° 30 ° 15 ° 90 ° 0 °

41. Polygons Drawing Quadrilateral Step 4: Use a ruler mark points C and D which are 3 cm from B and A. A B D C 6 cm 3 cm 3cm

42. Polygons Drawing Quadrilateral Step 5: Join points C and D with a straight line using a ruler. The line CD should be 6 cm in length. A B D C 6 cm 6 cm 3 cm 3 cm

43. Polygons Drawing Quadrilateral Step 6: Complete the figure. A B D C 6 cm 3 cm 6 cm 3 cm

44. Polygons Geometric Properties of Different Types of Quadrilaterals. *Opposite sides are equal and parallel -no line of symmetry *Opposite sides are equal and parallel *Each angle is 90° - 2 lines of symmetry *All sides are equals. *Opposite sides are parallel *Each angle is 90° -4 lines of symmetry Square Rectangle Parallelogram

45. Polygons Geometric Properties of Different Types of Quadrilaterals. *Has one pair of parallel opposite sides which do not have the same length -no line symmetry . *All sides are equals. *Opposite sides are parallel *Opposite angles are equal in size -2 lines of symmetry Trapezium Rhombus

46. Polygons Solving Problems Involving Quadrilaterals The sum of the angles of a quadrilateral is 360°. a+b+c+d = 360 ° a+b+c+d=360 ° a=c, b=d. a+b+c+d=360 ° a b c d a b c d a b c d < < < <

47. Polygons Solving Problems Involving Quadrilaterals Calculate the value of x in the diagram below. Solution: x+x+58°+62° = 360 ° 2x = 360°- 58 °- 62° = 240 ° x = 240° ÷ 2 = 120° x x 62 ° 58 °

48. Glossary A triangle has three sides of equal length and each angle is equal to 60° Equilateral triangle A unit for measuring angles Degree A diagram of figure whose sides begin and at the same point Closed diagram An amount of turn measured in degrees Angle Next to Adjacent A triangle with all three inside being acute Acute Triangle An angle that is less than 90 ° Acute Angle Description Item

49. Glossary A triangle with two equal sides Isosceles triangle Lines that cut across or cross each other Intersecting line A polygon with six sides Hexagon A polygon with seven sides Heptagon Characteristic of a figure or solid based on regular lines or shapes. Geometric properties Another name of a number, digit, line, shape or object. Figure Description Item

50. Glossary Two or more lines that go in exactly the same direction and are at the same distance apart at every point, so the lines never meet. Parallel lines A polygon with eight sides. Octagon An angle greater than a right angle (90°) but less than the angle the angle of a straight line (180°) Obtuse angle The line which divides something in half so that one half is exactly the same as the other half . Line of symmetry A long thin mark drawn on a surface. It can be straight or curved. It has no thickness and no dimension. Line Description Item

51. Glossary A plane figure or shape having four sides. Quadrilateral An instrument used to measure and draw angles. Protractor A plane shape or a closed figure with three or more straight sides. Polygon Lines that intersect to make right angles. Perpendicular lines A polygon with five sides Pentagon A plane figure with four sides, having parallel and equal opposite sides. Parallelogram Description Item

52. Glossary A triangle with each side different in length. Scalene triangle A triangle with a right angle. Right-angle triangle An angle measuring exactly 90°. Right angle Parallelogram with four equal sides. Rhombus An angle greater than the angle of a straight line (180°) but less than one whole turn or revolution Reflex angle A four-sided polygon with two pairs of equal and parallel sides and four right angles. Rectangle Description Item

53. Glossary A polygon with three sides. Triangle A plane figure with four sides where one pair of sides is parallel and the other pair is not. Trapezium Similarity of form on either side of a dividing line. Symmetry A quadrilateral having four equal sides and four right angles. Square A simple quickly-made drawing that does not show much detail. Sketch The outer form of a figure Shape Description Item

54. Glossary The plural of vertex. Vertices When two lines intersect, they form four angles at the vertex. The angles opposite each equal in size and are called vertically opposite angles Vertically opposite angles The point where two adjacent lines meet to form an angle, where three of more edges meet to form a corner. Vertex Description Item

55. Quick Exercise