Grade 7 Symmetry Chapter Test 2025-2026

Max marks: 30 Duration 1hr

Answer the following

One mark questions (1 x 15 = 15 marks)

1. Tick the correct option.

(i) Which of the following letters does not have reflection symmetry?

(a) A (b) Y (c) H (d) P

(ii) An equilateral triangle has rotational symmetry of order:

(a) 1 (b) 2 (c) 3 (d) 4

(iii) How many axes of reflection symmetry does a square have?

(a) 1 (b) 2 (c) 3 (d) 4

(iv) How many axes of symmetry does a circle have?

(a) 1 (b) 0 (c) 360 (d) infinite

(v) Which of these cannot be the angle of rotational symmetry?

(a) 180° (b) 90° (c) 240° (d) 120°

(vi) How many axes of symmetry does a scalene triangle have?

(a) 1 (b) 0 (c) 2 (d) 3

(vii) The number of axes of reflection symmetry and the order of rotational symmetry of the letter X are resp,:

(a) 2 and 4 (b) 1 and 2 (c) 4 and 2 (d) 1 and 4

2. Write against each statement whether it is true or false.

(i) Only round shapes can have rotational symmetry.

(ii) Every shape has a rotational symmetry of order 1 at least.

(iii) A shape with one line of symmetry cannot have a rotational symmetry of order greater than 1.

(iv) A shape with a larger degree of rotational symmetry has a greater order of symmetry.

(v) A semicircle has rotational symmetry of order 2.

3. Answer the following

(i) Name a shape that has the same number of lines of symmetry as a rectangle.

(ii) Draw a shape that has the same number of lines of symmetry as a square.

(iii) Does a spiral have rotational symmetry of order greater than 1?

(iv) How many lines of symmetry does each of the two set squares in the geometry instruments box have?

(v). How many lines of symmetry does the Indian national flag have?

(vi) .Draw any shape that has reflection symmetry but no rotational symmetry greater than 1.

(vii) Among the letters E, X, F, G, H, T, R and U, identify the letters having rotational symmetry and find their order of rotational symmetry.

(viii) Name an irregular polygon (all sides do not have the same length) (a) having reflection symmetry and (b) not having reflection symmetry.

Two marks questions (2 x 2 =04 marks)

1 Draw stars having five, six and seven arms. Find out whether each has rotational symmetry and if so, of what order.

Three mark questions (2 x 3 = 06 marks)

2. Fill in the numbers

DOWNLOAD THE QUESTION PAPER CLICK HERE

SOLUTIONS

Q1.

(i) Which of the following letters does not have reflection symmetry?

(d) P ✅

Explanation: 'A', 'Y', and 'H' have at least one line of symmetry. 'P' has none.

(ii) An equilateral triangle has rotational symmetry of order:

(c) 3 ✅

Explanation: It looks the same after rotating 120°, 240°, and 360°.

(iii) How many axes of reflection symmetry does a square have?

(d) 4 ✅

Explanation: A square has 2 diagonals and 2 midlines as symmetry axes.

(iv) How many axes of symmetry does a circle have?

(d) infinite ✅

Explanation: A circle can be folded about any diameter, giving infinite lines of symmetry.

(v) Which of these cannot be the angle of rotational symmetry?

(c) 240° ✅

Explanation: 240° is not a factor of 360° that evenly divides the circle into identical sections. (Corrected: Actually, 240° can be a rotational symmetry angle—see clarification below.)

⚠️ Correction: All listed angles can be rotational symmetry angles, depending on the shape. A regular hexagon, for instance, has 60°, 120°, 180°, 240°, 300°, and 360° rotational symmetry.
Therefore, a better correct answer does not exist from the given options unless the question specifies regular polygons only. In standard multiple-choice format, the best choice might be none of these or question should be revised.

(vi) How many axes of symmetry does a scalene triangle have?

(b) 0 ✅

Explanation: A scalene triangle has all unequal sides and angles—no symmetry.

(vii) The number of axes of reflection symmetry and the order of rotational symmetry of the letter X are respectively:

(a) 2 and 4 ✅

Explanation: 'X' has 2 axes of symmetry (vertical and diagonal) and rotational symmetry of order 4 (every 90°).

2. Write True or False for each statement:

(i) Only round shapes can have rotational symmetry.
→ False

Explanation: Many non-round shapes (like equilateral triangles, squares, etc.) have rotational symmetry.

(ii) Every shape has a rotational symmetry of order 1 at least.
→ True

Explanation: Every shape can be rotated by 360° to look the same — this is order 1 rotational symmetry.

(iii) A shape with one line of symmetry cannot have a rotational symmetry of order greater than 1.
→ True

Explanation: Shapes like an isosceles triangle have one line of symmetry and no rotational symmetry beyond order 1.

(iv) A shape with a larger degree of rotational symmetry has a greater order of symmetry.
→ True

Explanation: The order of rotational symmetry increases as the shape repeats more times during a 360° rotation.

(v) A semicircle has rotational symmetry of order 2.
→ False

Explanation: A semicircle has no rotational symmetry beyond order 1; it looks different when rotated before 360°.

3. Answer the following:

(i) Name a shape that has the same number of lines of symmetry as a rectangle.
→ Answer: Rhombus

Explanation: A rectangle has 2 lines of symmetry (horizontal and vertical), same as a rhombus (diagonals).

(ii) Draw a shape that has the same number of lines of symmetry as a square.
→ Answer: You can draw a regular cross (+) or a regular octagon. Both can have 4 lines of symmetry like a square.

(iii) Does a spiral have rotational symmetry of order greater than 1?
→ Answer: No

Explanation: A spiral has rotational pattern but not exact symmetry — it doesn’t look identical after a certain degree of rotation.

(iv) How many lines of symmetry does each of the two set squares in the geometry box have?
→ Answer:

45°–45°–90° set square: 1 line
30°–60°–90° set square: 0 lines

Explanation: The first has reflection symmetry along the perpendicular bisector of the right angle; the second does not.

(v) How many lines of symmetry does the Indian national flag have?
→ Answer: 1 line (vertical, through the center of the Ashoka Chakra)

Explanation: The three horizontal bands are symmetric top to bottom only if the Ashoka Chakra is centered.

(vi) Draw any shape that has reflection symmetry but no rotational symmetry greater than 1.
→ Answer: An isosceles triangle fits this.

(vii) Among the letters E, X, F, G, H, T, R, U, identify the letters having rotational symmetry and find their order of rotational symmetry:

X → Order 2
H → Order 2
U → Order 2

Other letters (E, F, G, T, R) do not have rotational symmetry beyond order 1.

(viii) Name an irregular polygon (all sides do not have the same length):

(a) Having reflection symmetry → Isosceles trapezium
(b) Not having reflection symmetry → Scalene triangle

Two marks questions (2 x 2 =04 marks)

1 Draw stars having five, six and seven arms. Find out whether each has rotational symmetry and if so, of what order.

⭐ Five-arm star:

A regular 5-point star (like the one on many flags).
Rotational Symmetry: Yes
Order: 5

You can rotate it 72°, 144°, 216°, 288°, and 360°, and it looks the same each time.

⭐ Six-arm star:

Can be drawn by overlapping two equilateral triangles (like the Star of David).
Rotational Symmetry: Yes
Order: 6

It looks the same every 60° rotation.

⭐ Seven-arm star:

A regular star with 7 equally spaced points (harder to draw perfectly by hand).
Rotational Symmetry: Yes
Order: 7

It repeats every 360° ÷ 7 ≈ 51.43°

2. Draw the line(s) of symmetry and write the order of rotational symmetry:

(i) House Shape (Pentagon with triangle on top):

Lines of symmetry: 1 (vertical line down the center)
Order of rotational symmetry: 1

It looks the same only after a full 360° rotation.

(ii) 5-pointed star:

Lines of symmetry: 5 (each passing through a point and opposite indentation)
Order of rotational symmetry: 5

Rotational symmetry every 72° (360° ÷ 5).

(iii) Regular Pentagon with 5 circles on vertices:

Lines of symmetry: 5
Order of rotational symmetry: 5

Three-mark questions:

Find the order of rotational symmetry of the following figures:

(i) Letter Z shape with embellishment:

Order of rotational symmetry: 2

It looks the same after 180°.

(ii) Star-shaped polygon (likely regular):

Order of rotational symmetry: 4

It repeats every 90°.

(iii) Plus-shaped design with 4 arms:

Order of rotational symmetry: 4

Same after 90°, 180°, 270°, and 360°.

(iv) Overlapping equilateral triangles (Star of David):

Order of rotational symmetry: 6

Rotational symmetry every 60°.

Letter	Number of Lines of Symmetry	Order of Rotational Symmetry
B	1 (vertical)	1
E	1 (vertical)	1
H	2 (vertical and horizontal)	2
M	1 (vertical)	1
N	0	1
O	Infinite	Infinite (or undefined / all angles)
Z	0	2

Notes:

B, E, M: Only have vertical symmetry.
H: Symmetrical both vertically and horizontally, and looks the same after a 180° rotation.
N and Z: Have no lines of symmetry, but Z has rotational symmetry of order 2 (180°).
O: A perfect circle has infinite symmetry lines and infinite rotational symmetry.

🌈⚡Key To Enjoy Learning Maths☘🌈

Tuesday, May 6, 2025