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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?