Chapter 14: Symmetry - Mock Test
Instructions
- •This test has 20 questions covering all topics from Chapter 14
- •Section A: 8 questions × 1 mark = 8 marks
- •Section B: 8 questions × 2 marks = 16 marks
- •Section C: 4 questions × 4 marks = 16 marks
- •No negative marking
Section A (1 mark each)
8 questions × 1 mark = 8 marks
1. How many lines of symmetry does a square have?
Answer: 4 (2 diagonals + 2 midlines)
2. What is the rotational order of an equilateral triangle?
Answer: 3 (rotates by 120°)
3. Does a scalene triangle have line symmetry?
Answer: No (all sides are unequal)
4. How many lines of symmetry does a rectangle have?
Answer: 2 (horizontal and vertical midlines)
5. If rotational order = 6, what is rotation angle?
Answer: 60° (360° ÷ 6 = 60°)
6. How many lines of symmetry does an isosceles triangle have?
Answer: 1 (from apex to base midpoint)
7. Does a circle have rotational symmetry?
Answer: Yes, infinite order (any angle rotation)
8. What is the rotational order of a rhombus?
Answer: 2 (180° rotation about center)
Section B (2 marks each)
8 questions × 2 marks = 16 marks
9. Draw a rectangle and mark its lines of symmetry.
Answer: Draw rectangle ABCD. Two lines: horizontal (through AB-CD midpoints) and vertical (through BC-AD midpoints).
10. A regular pentagon has which symmetry properties?
Answer: 5 lines of symmetry (from each vertex), rotational order 5 (72° rotation).
11. Explain why a parallelogram has rotational but not line symmetry.
Answer: When rotated 180° about center, it matches itself. But no single line divides it into identical halves.
12. How many lines and rotational order for a regular hexagon?
Answer: 6 lines of symmetry, rotational order 6 (60° rotation). 360° ÷ 6 = 60°
13. Compare symmetries of equilateral triangle and square.
Answer: Triangle: 3 lines, order 3. Square: 4 lines, order 4. Both have both types of symmetry.
14. Does a butterfly have rotational symmetry? Explain.
Answer: No. Butterfly has left-right mirror symmetry but doesn't look same when rotated.
15. A regular polygon has 8 lines of symmetry. How many sides?
Answer: 8 sides (regular octagon). For regular n-gon: n lines of symmetry and order n.
16. Explain why a circle has infinite symmetry.
Answer: Every diameter is a line of symmetry. Any rotation angle (no matter how small) matches the circle.
Section C (4 marks each)
4 questions × 4 marks = 16 marks
17. Analyze the symmetry of a square in detail: lines of symmetry, rotational order, center, and formulas.
Answer: 4 lines (2 diagonals AC and BD, 2 midlines). Order = 4, angle = 360÷4 = 90°. Center = intersection of diagonals. All 4 vertices map to each other.
18. Create a comparison table for symmetries of equilateral triangle, square, and regular hexagon with all properties.
Answer: Triangle (3 lines, order 3, 120°). Square (4 lines, order 4, 90°). Hexagon (6 lines, order 6, 60°). Pattern: n-gon has n lines, order n.
19. Which quadrilateral (square, rectangle, rhombus, parallelogram) has which symmetry? Justify each.
Answer: Square (4 lines, order 4). Rectangle (2 lines, order 2). Rhombus (2 lines [diagonals], order 2). Parallelogram (no lines, order 2 [180°]).
20. Explain with examples: relationship between order of symmetry and rotation angle. Verify with regular polygons.
Answer: Order = 360° ÷ angle. Pentagon: order 5, angle 72°. Hexagon: order 6, angle 60°. n-gon: order n, angle 360/n°.
Preparation Tips
- • Memorize symmetries of common shapes: square, rectangle, triangles, regular polygons
- • Use the formula: Order = 360° ÷ rotation angle
- • Rectangles have 2 lines (not 4 like squares) - common mistake
- • Not all symmetric figures have both types of symmetry
- • Practice drawing symmetry lines and identifying rotation centers