Symmetry

Exercise 14.2

Question 1: Which of the following figures have rotational symmetry of order more than 1:

line symmetry figure line symmetry figure line symmetry figure

line symmetry figure line symmetry figure line symmetry figure

Answer: a, b, d, e, f

Question 2: Give the order of rotational symmetry for each figure:

line symmetry figure line symmetry figure line symmetry figure line symmetry figure line symmetry figure line symmetry figure line symmetry figure line symmetry figure

Answer: (a) 2, (b) 2, (c) 3, (d) 4, (e) 4, (f) 5, (g) 6, (h) 3


Exercise 14.3

Question 1: Name any two figures that have both line symmetry and rotational symmetry.

Answer: Square, circle

Question 2: Draw, wherever possible, a rough sketch of

  1. A triangle with both line and rotational symmetries of order of more than 1.

    Answer: Equilateral triangle

  2. A triangle with only line symmetry and no rotational symmetry of order more than 1.

    Answer: Isosceles triangle

  3. A quadrilateral with rotational symmetry of order more than 1 but not a line of symmetry.

    Answer: Parallelogram

  4. A quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

    Answer: Kite


Question 3: If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than?

Answer: Yes

Question 4: Fill in the blanks:

Answer:

ShapeCentre of rotationOrder of rotationAngle of rotation
SquareIntersection point of diagonals490°
RectangleIntersection point of diagonals2180°
RhombusIntersection point of diagonals2180°
Equilateral triangleIntersection point of medians3120°
Regular hexagonIntersection point of diagonals660°
CircleCentreInfiniteAny angle
SemicircleCentre1360°


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