POLYGONS: TYPES OF TRIANGLES

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3. TYPES OF POLYGONS Triangle 3 sides Pentagon 5 sides Hexagon 6 sides Quadrilateral 4 sides Decagon 10 sides Heptagon 7 sides Octagon 8 sides Nonagon 9 sides

4. PARTS OF A POLYGONS SIDE/EDGE/LENGTH VERTEX/CORNER ANGLE

5. WHAT ARE POLYGONS • A many-sided figure • A flat shape with three(3) or more sides. • They are made from lines so they are classed as polygons. • The word Polygon comes from greek roots • Poly- means "many" and -gon means "angle". Hence, a polygon can also be called a flat shape with many angles.

6. PROPERTIES OF POLYGON: FUN FACTS • Polygons only have straight sides. • They don’t have curves and are not circles. • Polygons are closed shapes • Polygons sides join at corners.

7. Regular and Irregular Polygons REGULAR POLYGON – A polygon with all its side equal. IRREGULAR POLYGON – A polygon with sides unequal

8. POLYGONS NOT A POLYGON This shape has a curve NOT A POLYGON It is an open shape POLYGON Is a close shape Has straight sides

9. TYPES OF POLYGONS

11. WHAT IS A TRIANGLE? • A triangle is a three sided shape or polygon. • A Triangle has three (3) sides and three (3) angles • The sum of the angles in a triangle = 180° (All angles in a triangle add up to 180°) • Therefore: If any angle is missing in a triangle, I minus the given angles from 180° to find it.

12. HYPOTENUSE (Slanted Line) VERTICAL HEIGHT (Top to Bottom) BASE (Bottom) • The HEIGHT of the TRIANGLE is the VERTICAL • or PERPENDICULAR HEIGHT • (NOT the slanted part/line)

13. THREE (3) SIDED POLYGONS Equilateral Scalene Isosceles Three sided polygons are TRIANGLES:TRI – means three Right angled Acute-angled Obtuse-angled

14. EVERY TRIANGLES HAS TWO NAMES Every Triangle can have two names Its Side Name : Equilateral Triangle , Isosceles Triangle, Scalene Triangle Its Angle Name : Acute Angled Triangle, Right Angled Triangle, Obtuse Angled Triangle

15. Classifying Triangles by Sides Equilateral Isosceles Scalene

16. Classifying Triangles by Angles Obtuse-angled Right angled Acute-angled

17. TYPES OF TRIANGLES Equilateral Isosceles Scalene Acute angled Right angled Obtuse angled

19. SIDE or LENGTH

20. HEIGHT, HYPOTENUSE AND BASE

21. HEIGHT AND BASE

22. AREA

23. PERIMETER

24. CLASSIFYING TRIANGLES BY SIDES Equilateral Isosceles Scalene

25. EQUILATERAL TRIANGLES PROPERTIES OF EQUILATERALS • All sides of equal length • Three equal acute angles = 60° • Sum of angles = 180° • Is a regular polygon • Has 3 lines of symmetry

26. EQUILATERAL TRIANGLES 60° 7cm 7cm 60° 60° a 7cm Three equal acute angles=60° Three equal acute angles All sides of equal length a a Three lines of symmetry

27. THE EQUILATERAL TRIANGLE Each angles shows “a”. This means that all the angles are equal. • 3 equal sides • 3 equal angles • All angles acute • Each angle is 60 degrees • 3 lines of symmetry a a a Each side has this short line passing through it. This means that all the sides are equal.

28. ISOSCELES TRIANGLES PROPERTIES OF ISOSCELES • Two sides of equal length • Two angles (usually base) are equal • Sum of angles = 180° • Has 1 lines of symmetry

29. ISOSCELES TRIANGLES 7cm 7cm 7cm 7cm b a a 6cm 6cm Two sides equal length Two equal angles One line of symmetry

30. THE ISOSCELES TRIANGLE • 2 equal sides • 2 equal angles (usually the base/bottom angles) • 1line of symmetry shows that one angle is different shows that one side is different b a shows that two angles are equal. shows that two of the sides are equal. b a a a

31. SCALENE TRIANGLES PROPERTIES OF SCALENES • 3 unequal sides • 3 unequal angles • May have obtuse/right angle • Sum of angles = 180 ° • No Lines of symmetry

32. THE SCALENE TRIANGLE • 3 unequal sides • 3 unequal angles • No of lines of symmetry Notice that the dashes on the lines and the different letters show that the angles and sides are all different. a b c

33. CLASSIFYING TRIANGLES BY ANGLES Obtuse-angled Right angled Acute-angled

34. ACUTE-ANGLED TRIANGLES • PROPERTIES OF ACUTE-ANGLED • All its angles are acute • Can be a equilateral or scalene • Sum of angles = 180 °

35. ACUTE ANGLED TRIANGLE • All the angles in these triangles are acute • They are less than 90º

36. RIGHT-ANGLEDTRIANGLES • PROPERTIES OF Right-angled • One of the angles is equal to 90° • Can be an isosceles or scalene • Sum of angles = 180 °

37. RIGHT ANGLED TRIANGLE • Has ONE angle which is a right angle = equal to 90º

38. OBTUSE- ANGLED TRIANGLES • PROPERTIES OF OBTUSE-ANGLED • Has one obtuse angle • Sum of angles = 180 °

39. OBTUSE ANGLED TRIANGLE • Has ONE angle which is obtuse = more than 90° but less than 180° (> 90° but < 180°)

40. EXAMPLE OF TRIANGLES

41. EXAMPLE OF TRIANGLES IN THE WORLD

42. FOR TRIANGLES You can easily tell if your triangle is a equilateral , isosceles or scalene. • If it has all equal angles or all equal sides – it is an equilateral • If it has two equal angles or two equal sides – it is an isosceles • If it has no equal angles or no equal sides – it is a scalene. • If it has all angles less than 90° it is an acute angled triangle. • If it has one right angle in it. It is a right angled triangle. • If it has one obtuse angle in it. It is an obtuse angled triangle.

43. State the type of triangles in the following Name them by BOTH Sides and Angles The first one is done for you.

44. STATE THE TYPE OF TRIANGLE By side : By angle: By side : By angle:

45. ANSWER: STATE THE TYPE OF TRIANGLE By side : scalene By angle: acute-angled By side : scalene By angle: obtuse- angled

46. STATE THE TYPE OF TRIANGLE By side : By angle: By side : By angle:

47. ANSWER: STATE THE TYPE OF TRIANGLE By side : scalene By angle: acute-angled By side : scalene By angle: obtuse- angled

48. STATE THE TYPE OF TRIANGLE By side : By angle: By side : By angle:

49. ANSWER: STATE THE TYPE OF TRIANGLE By side : isosceles By angle: acute-angled By side : isosceles By angle: obtuse- angled

50. STATE THE TYPE OF TRIANGLE By side : By angle: By side : By angle: