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- 1. Chapter 8: Shapes and symmetry By: Eng./Teacher Wael Shnoudi
- 2. 8.1 Quadrilaterals and polygons
- 3. Objectives 01 02 Recognize line symmetry and rotational symmetry in 2D shapes, and identify different properties of 2D shapes identify and describe the hierarchy of quadrilaterals.
- 4. Lines of Symmetry • A line that can be drawn through a shape so that what can be see on either side is a mirror image. • It is sometimes called a Mirror Line
- 5. These shapes have one line of symmetry
- 6. These shapes have two lines of symmetry
- 7. Some shapes have more than 2 lines of symmetry Square Equilateral Triangle Circle
- 8. Rectangle 2 lines of symmetry Square 4 lines of symmetry Rhombus 2 lines of symmetry Equilateral Triangle 3 lines of symmetry Isosceles triangle 1 line of symmetry Isosceles Trapezium 1 line of symmetry Kite 1 line of symmetry Trapezium No lines of symmetry Parallelogram no lines of symmetry Regular Pentagon 5 lines of symmetry Regular Hexagon 6 lines of symmetry Regular Heptagon 7 lines of symmetry The number of lines of symmetry in a regular polygon is equal to the number of sides.
- 9. Rotational Symmetry A square has a rotational symmetry of order 4
- 10. Rotational Symmetry • Rotational Symmetry is how many times a shape can be rotated and fit within itself/how many times a shape can be rotated and look the same
- 11. Equilateral Triangle An equilateral triangle has a rotational symmetry of order 3
- 12. What is the rotational symmetry of this shape? It has to be rotated one complete turn before it fits into itself Order 1
- 13. Shapes and Symmetry
- 14. These figures are not polygons These figures are polygons Definition:A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. Polygons
- 15. Classifications of a Polygon Regular: A polygon in which all angles are congruent and all sides are congruent That’s an equiangular equilateral polygon. Irregular: A polygon that is not regular
- 17. Refer to book
- 18. What is a Quadrilateral? • A quadrilateral is a two-dimensional figure with four sides and four angles. • The word part “quad” means 4 and “lateral” means sides.
- 19. Quadrilaterals in the real world
- 20. Types of Quadrilaterals Square Rectangle Trapezoid Rhombus Paralellogram Kite
- 21. A SQUARE • A square is a quadrilateral with 4 equal sides and 4 right angles.
- 22. A RECTANGLE • A rectangle is a quadrilateral with 4 right angles. • Its opposite sides are equal and parallel.
- 23. Is a square a rectangle? REMEMBER: • A rectangle is a quadrilateral with 4 right angles. Its opposite sides are equal and parallel. • A square is a quadrilateral with 4 equal sides and 4 right angles. Rectangle?
- 24. Is a rectangle a square? REMEMBER: • A rectangle is a quadrilateral with 4 right angles. Its opposite sides are equal and parallel. • A square is a quadrilateral with 4 equal sides and 4 right angles. Square?
- 25. Determination….. • A square can also be called a rectangle because it has four right angles and its opposite sides are equal and parallel. A rectangle is NOT a square because it does not have equal sides.
- 26. A TRAPEZOID • A trapezoid is a quadrilateral that has exactly 1 pair of parallel sides.
- 27. IS THIS A TRAPEZOID? ◦ Yes, it has one set of parallel sides.
- 28. A RHOMBUS • A rhombus is a quadrilateral that has 4 equal sides. Its opposite sides are parallel.
- 29. A PARALLELOGRAM • A parallelogram is a quadrilateral that has opposite sides that are equal and parallel. • Which of the quadrilaterals we have seen are parallelograms?
- 30. Properties of quadrilaterals
- 31. Have 4 sides and 4 angles Has opposite sides that are equal and parallel. Has 1 pair of parallel sides. Has 4 right angles. Opposite sides are equal and parallel. Has 4 equal sides. Opposite sides are parallel. Has 4 equal sides and 4 right angles. What conclusions can we draw from the graphic?
- 32. A square can also be called a rhombus, a rectangle, a parallelogram, and a quadrilateral. A rectangle can also be called a parallelogram and a quadrilateral. A rhombus can also be called a parallelogram and a quadrilateral. A parallelogram can also be called a quadrilateral. A trapezoid is a quadrilateral. Have 4 sides and 4 angles Has opposite sides that are equal and parallel. Has 1 pair of parallel sides. Has 4 right angles. Opposite sides are equal and parallel. Has 4 equal sides. Opposite sides are parallel. Has 4 equal sides and 4 right angles.
- 33. Rectangle 2 pairs of sides of equal length 2 pairs of parallel sides All angles 90° Diagonals that bisect each other 2 lines of symmetry Order 2 rotational symmetry Square All sides have the same length All angles 90° 2 pairs of parallel sides Diagonals that bisect each other at 90° 4 lines of symmetry Order 4 rotational symmetry •Properties of Quadrilaterals. •A quadrilateral is an enclosed 4-sided flat shape. •The angle sum of any quadrilateral is 360°. Parallelogram 2 pairs of sides of equal length 2 pairs of parallel sides Opposite angles are equal Diagonals bisect each other Sum of any two adjacent angles is 180° No lines of symmetry Order 2 rotational symmetry Rhombus All sides have the same length 2 pairs of parallel sides Opposite angles are equal Diagonals bisect each other perpendicularly at 900 Sum of any two adjacent angles is 180° 2 lines of symmetry Order 2 rotational symmetry
- 34. •Properties of Quadrilaterals. •A quadrilateral is an enclosed 4-sided flat shape. •The angle sum of any quadrilateral is 360°. Kite 2 pairs of equal sides No parallel sides 1 pair of equal angles 1 diagonal that bisects the other Diagonals cross at 90° 1 line of symmetry Order 1 rotational symmetry Trapezium Sides of different lengths Only one pair of parallel sides Angles of different sizes No lines of symmetry Order 1 rotational symmetry Isosceles Trapezium 2 equal sides Only one pair of parallel sides 2 pairs of equal angles 1 line of symmetry Order 1 of rotational symmetry
- 35. Book page 175-176
- 36. They are all equal. is the same as/equal to is the same as/equal to Book page 175-176
- 37. 11 12 Book page 175-176
- 38. True False, AB is parallel to CD False, BD is parallel to AC True SS # 8 Page 6/ Book page 176
- 39. Book page 176
- 40. Book page 176
- 41. A square is a special rectangle. A rectangle is a special parallelogram. A rhombus is a special parallelogram. A square is a special rhombus. Book page 177
- 42. Example: No she hasn’t. She could be describing either a rectangle or a square. She also needs to say that all the sides have the same length. Book page 177
- 43. False. AC is the same length as BD True False. Angle CAB is the same size as angle ABD True Book page 178
- 44. • one pair of sides the same length • one pair of parallel sides • two pairs of equal angles. Book page 178
- 45. An isosceles trapezium is always a trapezium but a trapezium is not always an isosceles trapezium. A rhombus is a special kite. A parallelogram is a special trapezium. Book page 179
- 46. Example: No, he hasn’t. He has said that the kite has two pairs of equal angles, but it only has one pair of equal angles. Book page 179
- 47. J K N L I M H
- 48. True False True
- 49. ANY QUESTIONS?