CBSE Class 7 Mathematics Symmetry Assignment Set 01

Question 1. Define symmetrical figures. Draw two figures which are symmetrical.
Answer: A figure is said to be symmetrical if it can be divided into two identical and matching halves that fit exactly over each other when folded along a specific line (axis of symmetry).
Examples of symmetrical figures include an equilateral triangle and a circle.
In simple words: A symmetrical figure looks identical on both sides when folded in half.

Exam Tip: Always mention that the two halves must coincide completely for a figure to be symmetrical.

Question 2. What do you mean by a line of symmetry? Draw a figure with line(s) of symmetry on it.
Answer: A line of symmetry (or axis of symmetry) is a straight line that divides a given figure into two parts such that each part is the exact mirror image of the other.
For example, a rectangle has 2 lines of symmetry (one horizontal and one vertical passing through the center).
In simple words: The fold line that cuts a shape into two equal, matching mirror halves is called the line of symmetry.

Exam Tip: Use a dotted line to represent the line of symmetry in geometrical diagrams.

Question 3. In the following figures, the lines of symmetry is given as a dotted line. Complete each figure performing reflection in the dotted line.
(a) b) c)
Answer: To complete each figure, draw the mirror reflection of the given half across the dotted vertical line of symmetry, ensuring that corresponding points are equidistant from the dotted line.
- For figure (a): The curved bulging side on the left is reflected across the vertical dotted line to form a symmetric curved shape.
- For figure (b): The asymmetric polygon shape on the left is mirrored across the vertical line.
- For figure (c): The triangular wedge pointing left is mirrored to form a complete symmetrical hexagonal or pointed arrow shape.
In simple words: Draw the exact mirror reflection on the other side of the dotted line to complete the shape.

Exam Tip: Ensure that the distance of each vertex from the dotted line of symmetry is equal on both sides.

Question 4. State the number of lines of symmetry for the following figures.
(a) An equilateral triangle
(b) A scalene triangle
(c) A quadrilateral
(d) A circle
(e) A regular hexagon
Answer:
(a) An equilateral triangle: 3 lines of symmetry
(b) A scalene triangle: 0 lines of symmetry
(c) A quadrilateral: 0 lines of symmetry (in general, unless specified as square, rectangle, rhombus, etc.)
(d) A circle: Infinite lines of symmetry
(e) A regular hexagon: 6 lines of symmetry
In simple words: Regular shapes have as many lines of symmetry as they have sides or equal parts.

Exam Tip: Memorize symmetry properties for regular polygons: a regular polygon of \(n\) sides has \(n\) lines of symmetry.

Question 5. What letters of the English alphabet have reflection symmetry about:
(a) A vertical mirror
(b) A horizontal mirror
(c) Both horizontal and vertical mirrors
Answer:
(a) A vertical mirror: A, H, I, M, O, T, U, V, W, X, Y
(b) A horizontal mirror: B, C, D, E, H, I, K, O, X
(c) Both horizontal and vertical mirrors: H, I, O, X
In simple words: Letters that look the same when reflected vertically, horizontally, or both.

Exam Tip: Write capital block letters in your exam when testing for symmetry lines.

Question 6. Give three examples of shapes with no line of symmetry.
Answer:
1. A scalene triangle
2. A parallelogram (that is not a rectangle or rhombus)
3. The letter "Z" (or "S", "F", "G", "J", "P", "Q", "R")
In simple words: Asymmetric shapes cannot be folded onto themselves in any direction.

Exam Tip: Scalene triangles and standard parallelograms are the safest standard examples of shapes with zero lines of symmetry.

Question 7. Give the order of Rotational symmetry for the following:
Z, H, C, (a) Four-petaled star/pinwheel, (b) Three-spoked steering wheel / Mercedes-like star, (c) Circle with 3 dividing lines
Answer:
- Letter Z: Order 2
- Letter H: Order 2
- Letter C: Order 1
- Figure (a) (Four-petaled star): Order 4
- Figure (b) (Three-spoked star): Order 3
- Figure (c) (Circle divided into 3 sectors): Order 3
In simple words: Order of rotational symmetry is the number of times a shape fits onto itself during one full \(360^{\circ}\) turn.

Exam Tip: Order of rotational symmetry is always at least 1 for any geometric shape.

Question 8. Name any two figures that have both line symmetry and rotational symmetry.
Answer:
1. An equilateral triangle (3 lines of symmetry, rotational symmetry of order 3)
2. A square (4 lines of symmetry, rotational symmetry of order 4)
(Other valid examples: Circle, regular hexagon, rhombus, rectangle)
In simple words: Regular polygons possess both line symmetry and rotational symmetry.

Exam Tip: Circles and regular polygons are universal examples that possess both types of symmetry.

Question 9. Draw, wherever possible, a rough sketch of:
(a) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(b) A triangle with only line symmetry and no rotational symmetry of order more than 1.
Answer:
(a) A parallelogram (which is not a rectangle or rhombus) has rotational symmetry of order 2, but it has no lines of symmetry.
(b) An isosceles triangle (which is not equilateral) has exactly 1 line of symmetry, but its rotational symmetry order is 1.
In simple words: (a) A parallelogram. (b) An isosceles triangle.

Exam Tip: Parallelograms rotate onto themselves after \(180^{\circ}\) (order 2) but cannot be folded symmetrically along any straight line.

Question 10. Fill in the blanks:
Answer:
The completed table of rotational symmetry properties is given below:

Exam Tip: Angle of rotation is calculated using the formula \(\text{Angle} = \frac{360^{\circ}}{\text{Order of Rotation}}\).