Class 9 Mathematics Chapter 9 Symmetry MCQ with Answers — 30 Solved Questions

The CBSE Class 9 Mathematics syllabus (2024–25) has shifted decisively toward objective assessment. Where descriptive exams once rewarded lengthy proofs, the new pattern tests conceptual clarity and problem-solving speed through multiple-choice questions. In Chapter 9 (Symmetry), this shift matters even more: symmetry is fundamentally about *recognizing* and *categorizing* transformations, not deriving them from first principles. A well-designed MCQ forces you to distinguish between line symmetry (reflection across a fixed axis), rotational symmetry (rotation by 360°/n degrees), and absence of symmetry—distinctions that might be glossed over in longer-form answers. Moreover, MCQs in the new CBSE pattern often test *conceptual traps*: a square has 4 lines of symmetry AND rotational symmetry of order 4, but a rhombus has only 2 lines of symmetry yet also rotational symmetry of order 2. Confusing these is exactly what trap options are designed to catch. By practicing 30 strategically-sequenced MCQs, you train your brain to read questions carefully, eliminate wrong answers with confidence, and manage exam time efficiently—three skills that collectively boost your score by 15–20% compared to unprepared attempts.

**Question 1:** Which of the following letters of the English alphabet has exactly one line of symmetry? (A) A (B) B (C) C (D) D **Answer:** (A) A **Reason:** The letter A is symmetric about a vertical line through its apex; B, C, and D lack any line of symmetry. **Question 2:** How many lines of symmetry does a circle have? (A) 1 (B) 2 (C) Infinite (D) 0 **Answer:** (C) Infinite **Reason:** Every diameter of a circle is a line of symmetry. **Question 3:** What is the order of rotational symmetry of an equilateral triangle? (A) 1 (B) 2 (C) 3 (D) 4 **Answer:** (C) 3 **Reason:** An equilateral triangle looks identical after rotation by 120°, 240°, and 360°. **Question 4:** Which quadrilateral has exactly two lines of symmetry? (A) Rectangle (B) Square (C) Rhombus (D) Kite **Answer:** (C) Rhombus **Reason:** A rhombus has 2 lines of symmetry (along its diagonals); a square has 4. **Question 5:** If a figure has rotational symmetry of order 2, by what angle must it rotate to look identical? (A) 90° (B) 180° (C) 270° (D) 360° **Answer:** (B) 180° **Reason:** Order 2 means 360° ÷ 2 = 180°. **Question 6:** The letter 'H' has how many lines of symmetry? (A) 0 (B) 1 (C) 2 (D) 3 **Answer:** (C) 2 **Reason:** H is symmetric about both a horizontal and a vertical line through its centre. **Question 7:** Which shape among the following has no line of symmetry? (A) Isosceles triangle (B) Scalene triangle (C) Right-angled isosceles triangle (D) Equilateral triangle **Answer:** (B) Scalene triangle **Reason:** A scalene triangle has all sides unequal, so no line of symmetry exists. **Question 8:** A rectangle has rotational symmetry of order: (A) 1 (B) 2 (C) 3 (D) 4 **Answer:** (B) 2 **Reason:** A rectangle looks identical after 180° rotation but not 90°. **Question 9:** How many lines of symmetry does a square have? (A) 2 (B) 3 (C) 4 (D) 5 **Answer:** (C) 4 **Reason:** 2 diagonal lines + 2 midline (horizontal and vertical). **Question 10:** The digit '8' has how many lines of symmetry? (A) 0 (B) 1 (C) 2 (D) Infinite **Answer:** (C) 2 **Reason:** The digit 8 is symmetric about both a vertical and horizontal axis through its centre.

**Question 11:** A regular hexagon has: (A) 6 lines of symmetry and rotational symmetry of order 6 (B) 3 lines of symmetry and rotational symmetry of order 3 (C) 6 lines of symmetry and rotational symmetry of order 3 (D) 12 lines of symmetry and rotational symmetry of order 12 **Answer:** (A) 6 lines of symmetry and rotational symmetry of order 6 **Reason:** A regular hexagon has 6-fold rotational symmetry (360° ÷ 6 = 60°) and 6 lines of symmetry (3 through opposite vertices, 3 through midpoints of opposite sides). **Question 12:** Which of the following statements is true? (A) Every figure with line symmetry also has rotational symmetry. (B) Every figure with rotational symmetry also has line symmetry. (C) A figure can have rotational symmetry without having any line of symmetry. (D) A figure must have both to be called 'symmetric'. **Answer:** (C) A figure can have rotational symmetry without having any line of symmetry. **Reason:** A swastika has 4-fold rotational symmetry but no line of symmetry. **Question 13:** An isosceles trapezium has: (A) 1 line of symmetry and rotational symmetry of order 1 (B) 1 line of symmetry and rotational symmetry of order 2 (C) 2 lines of symmetry and rotational symmetry of order 1 (D) 2 lines of symmetry and rotational symmetry of order 2 **Answer:** (A) 1 line of symmetry and rotational symmetry of order 1 **Reason:** An isosceles trapezium is symmetric about the perpendicular bisector of its parallel sides but has no rotational symmetry. **Question 14:** The letter 'N' has: (A) 1 line of symmetry and rotational symmetry of order 1 (B) 1 line of symmetry and rotational symmetry of order 2 (C) 0 lines of symmetry and rotational symmetry of order 2 (D) 0 lines of symmetry and rotational symmetry of order 1 **Answer:** (C) 0 lines of symmetry and rotational symmetry of order 2 **Reason:** 'N' becomes itself when rotated 180° but has no line of symmetry. **Question 15:** A regular pentagon has rotational symmetry of order: (A) 4 (B) 5 (C) 6 (D) 8 **Answer:** (B) 5 **Reason:** 360° ÷ 5 = 72° rotation gives 5-fold symmetry. **Question 16:** Which figure has the same number of lines of symmetry as its rotational symmetry order? (A) Square (B) Rectangle (C) Rhombus with 60° angle (D) Parallelogram **Answer:** (A) Square **Reason:** A square has 4 lines of symmetry and rotational symmetry of order 4. **Question 17:** A kite (like the paper toy) has: (A) 1 line of symmetry and rotational symmetry of order 1 (B) 2 lines of symmetry and rotational symmetry of order 2 (C) 1 line of symmetry and rotational symmetry of order 2 (D) 0 lines of symmetry and rotational symmetry of order 1 **Answer:** (A) 1 line of symmetry and rotational symmetry of order 1 **Reason:** A kite is symmetric about one diagonal but has no rotational symmetry. **Question 18:** The shape of a starfish (5-pointed star) has: (A) 5 lines of symmetry and rotational symmetry of order 5 (B) 10 lines of symmetry and rotational symmetry of order 10 (C) 5 lines of symmetry and rotational symmetry of order 1 (D) 0 lines of symmetry and rotational symmetry of order 5 **Answer:** (A) 5 lines of symmetry and rotational symmetry of order 5 **Reason:** A regular 5-pointed star has 5 axes of symmetry and 72° rotational symmetry. **Question 19:** Which of these has reflectional symmetry but NOT rotational symmetry (except order 1)? (A) Equilateral triangle (B) Right-angled isosceles triangle (C) Regular octagon (D) Square **Answer:** (B) Right-angled isosceles triangle **Reason:** A right-angled isosceles triangle has 1 line of symmetry (altitude from the right angle) but no rotational symmetry of order > 1. **Question 20:** A circle has: (A) Infinite lines of symmetry but no rotational symmetry (B) No lines of symmetry but infinite rotational symmetry (C) Infinite lines of symmetry and infinite rotational symmetry (D) Exactly 1 line of symmetry and rotational symmetry of order 1 **Answer:** (C) Infinite lines of symmetry and infinite rotational symmetry **Reason:** Every diameter is a line of symmetry; any angle of rotation preserves the circle's shape.

**Question 21:** **Assertion (A):** A rhombus always has rotational symmetry of order 2. **Reason (R):** A rhombus has two diagonals that bisect each other at right angles. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (A) Both A and R are true, and R is the correct explanation of A. **Reason:** The 180° rotational symmetry of a rhombus follows directly from its diagonal-bisection property. **Question 22:** **Assertion (A):** All regular polygons have the same number of lines of symmetry as their order of rotational symmetry. **Reason (R):** A regular polygon is defined as one with all sides and angles equal. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (B) Both A and R are true, but R is not the correct explanation of A. **Reason:** A is true (regular n-gon has n lines and order n symmetry), but the reason is a definition, not an explanation of symmetry. **Question 23:** **Assertion (A):** If a figure has rotational symmetry of order 3, it must have at least 3 lines of symmetry. **Reason (R):** Order of rotational symmetry always equals the number of lines of symmetry. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (D) A is false, but R is true. **Reason:** A swastika has rotational symmetry of order 4 but zero lines of symmetry; the assertion is false, making the reason irrelevant here. **Question 24:** **Assertion (A):** A letter 'Z' has no line of symmetry but has rotational symmetry of order 2. **Reason (R):** Line symmetry requires reflection across an axis; rotational symmetry requires the figure to look identical after a 180° rotation. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (A) Both A and R are true, and R is the correct explanation of A. **Reason:** Z matches itself at 180° but not across any line; the reason correctly explains both properties. **Question 25:** **Assertion (A):** An isosceles triangle has exactly one line of symmetry and no rotational symmetry (except order 1). **Reason (R):** The line of symmetry of an isosceles triangle passes through the vertex angle and the midpoint of the base. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (A) Both A and R are true, and R is the correct explanation of A. **Reason:** The axis of symmetry for an isosceles triangle is correctly described, and this fact confirms assertion A. **Question 26:** **Assertion (A):** A figure with rotational symmetry of order n (where n > 1) always has line symmetry if and only if n is odd. **Reason (R):** Regular polygons with an even number of sides always have lines of symmetry through opposite vertices and opposite edge midpoints. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (D) A is false, but R is true. **Reason:** Even n-gons like squares and hexagons have both rotational and line symmetry; assertion A is too restrictive. **Question 27:** **Assertion (A):** If a planar figure has exactly 2 lines of symmetry, it must have rotational symmetry of order 2. **Reason (R):** Two perpendicular lines of symmetry always guarantee 180° rotational symmetry. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (D) A is false, but R is true. **Reason:** A kite or isosceles trapezium can have 1 line of symmetry without rotational symmetry; assertion A is false, though the reason is geometrically sound in special cases. **Question 28:** **Assertion (A):** Among all quadrilaterals, only a square has exactly 4 lines of symmetry and rotational symmetry of order 4. **Reason (R):** A rectangle has 2 lines of symmetry and rotational symmetry of order 2. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (B) Both A and R are true, but R is not the correct explanation of A. **Reason:** Both statements are true, but R does not explain why the square is the *only* quadrilateral with those symmetries. **Question 29:** **Assertion (A):** A regular star polygon (like a five-pointed star) has the same number of lines of symmetry as a regular polygon with the same number of points. **Reason (R):** Both share the same central rotational angles. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (A) Both A and R are true, and R is the correct explanation of A. **Reason:** A 5-pointed star and a regular pentagon both have 5 lines of symmetry and 72° rotational symmetry. **Question 30:** **Assertion (A):** It is possible for a figure to have rotational symmetry of order 6 but only 3 lines of symmetry. **Reason (R):** A figure's rotational symmetry order and line symmetry count are independent properties. (A) Both A and R are true, and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. **Answer:** (D) A is false, but R is true. **Reason:** For regular n-gons, the two symmetry types always match; however, some non-regular figures could theoretically exhibit this pattern, making assertion A debatable in the strict NCERT context (false for standard figures).

CBSE MCQ setters are skilled at designing plausible wrong answers that exploit common misconceptions. Here are the five most frequent traps in Chapter 9: **Trap 1: Confusing 'line symmetry count' with 'rotational symmetry order'** Students often assume that if a figure has 3 lines of symmetry, it must have rotational symmetry of order 3. *False.* A kite has 1 line of symmetry and no rotational symmetry. Conversely, a swastika has rotational symmetry of order 4 but zero lines of symmetry. *Always check both properties separately.* **Trap 2: Assuming 'regular' automatically means both symmetries are equal** While true for regular polygons (square: 4 lines = order 4; regular hexagon: 6 lines = order 6), this breaks down for non-regular figures. An isosceles triangle has 1 line of symmetry but no rotational symmetry beyond order 1. *Read the problem carefully: is it 'regular'?* **Trap 3: Miscounting lines of symmetry in familiar shapes** Students often say a rectangle has 4 lines of symmetry (confusing it with a square). In fact, a rectangle has only 2 (horizontal and vertical midlines), not 4 (diagonals don't bisect symmetrically unless all sides are equal). *Draw it out or trace it mentally.* **Trap 4: Treating 'no rotational symmetry' as order 0, not order 1** Every figure has rotational symmetry of *order at least 1* (it looks identical after a 360° rotation). A figure with "no rotational symmetry" actually means *no rotational symmetry of order > 1.* The correct phrasing is "rotational symmetry of order 1." *Pay attention to wording.* **Trap 5: Assuming all quadrilaterals with 2 lines of symmetry have rotational symmetry of order 2** A kite has exactly 2 lines of symmetry (both diagonals if it's a rhombus, or 1 if it's not)—but a non-rhombus kite has *no* rotational symmetry. *Distinguish between kites, rhombuses, and rectangles carefully.* **Example Trap in Action:** *Question:* "An isosceles trapezium has...?" *Option A (TRAP):* 2 lines of symmetry and rotational symmetry of order 2. ← Confuses it with a rectangle. *Option B (TRAP):* 0 lines of symmetry and rotational symmetry of order 1. ← Denies its obvious vertical midline symmetry. *Option C (CORRECT):* 1 line of symmetry and rotational symmetry of order 1. ← Only the perpendicular bisector of the parallel sides is a line of symmetry. **Pro Tip:** When you see an option that "feels right but a little off," it's probably a trap. Read the question word-by-word, sketch the figure if time allows, and eliminate the most tempting wrong answer first. At cbsetutor.ai, our interactive quizzes highlight these traps in real-time with detailed explanations—try a free 3-day trial to see how this accelerates your mastery.

In a typical CBSE Class 9 Mathematics unit test, you'll face 25–30 MCQs in 40–50 minutes. Symmetry questions often appear in clusters (3–5 consecutive questions), and your speed and accuracy here directly impact your overall percentile. Here's the battlefield-tested strategy: **Phase 1: Skim & Sort (4 minutes)** Before you start solving, scan all Symmetry questions and mentally tag them: - **Green (Easy):** Single-property questions ("How many lines does X have?"). Solve first. - **Yellow (Medium):** Two-property or comparison questions. Solve second. - **Red (Hard):** Assertion-reason or complex scenarios. Solve last or revisit if time permits. This prevents you from spending 10 minutes on a hard trap question when two easy questions lie unsolved. **Phase 2: Easy Pass (8–10 minutes)** Solve 8–10 green-tagged questions *without* second-guessing. Your goal is speed + accuracy. Use the "sketch or trace" method: mentally rotate a square to confirm 4-fold symmetry, or reflect a kite across its diagonal to see the single line of symmetry. Do NOT get bogged down in over-analysis here. **Phase 3: Medium Pass (12–15 minutes)** Now tackle yellow questions. These often require you to *compare* two symmetry types or *combine* line and rotational properties. Spend 1.5–2 minutes per question. If you hit 90 seconds with no clarity, mark it for review and move on. Do *not* let a single question steal 5 minutes. **Phase 4: Hard Pass (10 minutes, or skip initially)** Assertion-reason questions demand careful reading. Read the assertion first, then the reason, *then* their relationship. If a question looks genuinely hard (unfamiliar shape, unusual phrasing), skip it during your first pass and return with fresh eyes if time remains. You'll often spot the trap more clearly on the second read. **Phase 5: Review & Guess (remaining time)** With 3–5 minutes left, revisit flagged questions. For *pure guesses*, never leave blanks; eliminate 1–2 obviously wrong options and choose the most geometry-aligned answer. **Critical Numbers to Memorize:** - Equilateral triangle: 3 lines, order 3. - Square: 4 lines, order 4. - Regular hexagon: 6 lines, order 6. - Regular pentagon: 5 lines, order 5. - Rectangle: 2 lines, order 2. - Rhombus: 2 lines, order 2. - Circle: ∞ lines, ∞ order. - Isosceles triangle: 1 line, order 1. - Scalene triangle: 0 lines, order 1. - Kite: 1 line, order 1. **Avoid These Time-Wasters:** 1. Obsessively redrawing figures—sketch once, trust your memory. 2. Reading every word of a 10-line scenario—skim to the core question. 3. Switching between options more than twice—second-guessing kills time. 4. Mental arithmetic for angle calculations—if rotational order is n, angle = 360°/n; trust the formula. **Real Example: How to Save 2 Minutes** *Question:* "Which of the following has 4 lines of symmetry and rotational symmetry of order 4?" *Time-optimal method:* - Recognize: Only square and regular octagon have order ≥ 4 symmetry. - Square has 4 lines + order 4. ✓ *Check answer.* - Regular octagon has 8 lines + order 8. ✗ - Answer: Square. ← 45 seconds, not 2 minutes of deliberation. With disciplined phase-wise solving and these shortcuts, you can comfortably attempt 25 questions in 40 minutes, scoring ≥90%.

You now have 30 NCERT-aligned MCQs across three tiers, plus strategies to avoid traps and manage your time under exam pressure. Here's how to weaponize this guide: **Day 1:** Solve all 10 Easy questions (should take 10–12 minutes). Review your answers. If you score <80%, re-read the foundational concepts in your NCERT textbook (Chapter 9, Section 9.1) before moving forward. **Day 2:** Tackle all 10 Medium questions (15–18 minutes). These test the critical distinction between line and rotational symmetry. If a question stumps you, pause and sketch the figure. *Do not skip.* **Day 3:** Attempt all 10 Hard questions (20–25 minutes). These are assertion-reason traps designed to catch careless readers. Read each assertion-reason pair twice before choosing. Record which traps caught you; these are your weak points. **Day 4 (Optional):** Mix and shuffle: create a randomized 15-question test from all three tiers. Time yourself: 20 minutes maximum. Aim for 14/15 (≥93%). **Beyond This Guide:** Symmetry extends beyond MCQs into your practical and descriptive work. After this week, engage with real-world symmetry: photograph symmetric buildings, patterns in nature, or rangoli designs. This *visual reinforcement* cements your intuition far better than question-drilling alone. Additionally, attempt past CBSE sample papers (available at cbsetutor.ai) to see how examiners vary symmetry question formats year after year. **Why This Matters:** Symmetry is not just a standalone topic—it bridges into Class 10 Geometry (congruent figures, transformations) and even Class 11 trigonometry (periodic functions as rotational symmetries). Master it now, and you'll find yourself solving harder problems faster in the years ahead. Start a 3-day free trial at cbsetutor.ai to access video explanations for each question, live doubt-clearing sessions with expert tutors, and curated practice sets tailored to your weak spots.