Class 6 Maths · Chapter 9
Short answer: Class 6 Maths Chapter 9 Symmetry NCERT Ganita Prakash ke solutions — line symmetry, rotational symmetry, aur lines of symmetry ke saare concepts step-by-step working ke saath, exam-ready format me.
Chapter 9 — Symmetry — Class 6 Ganita Prakash ka ek visual aur intuitive chapter hai jo bachchon ko geometric shapes, patterns, aur real-life objects me symmetry pehchaanna sikhata hai. Yeh chapter foundation banata hai jo aage Class 6 Maths chapter wise important questions me Lines and Angles aur Playing with Constructions jaise geometry-based chapters ke liye zaroori hoti hai.
Is chapter me do main concepts cover hote hain — line symmetry (jise reflection symmetry bhi kehte hain, jahan ek mirror line figure ko do exact matching halves me baant deti hai) aur rotational symmetry (jahan figure ko ek point ke around ghumane par 360° se kam angle pe woh apne original shape jaisi dikhti hai). NCERT Class 6 Maths Ganita Prakash chapter 1 patterns in mathematics solutions se bhi is chapter ka connection dikhta hai — dono hi chapters me pattern-recognition ek core skill hai. Jaise Class 6 Maths chapter 5 Prime Time Goldbach conjecture explanation numbers ke patterns dhoondhna sikhata hai, waise hi Symmetry shapes ke patterns dhoondhna sikhata hai.
Chapter 9 Summary — 5 Minute Revision
Symmetry chapter Class 6 Ganita Prakash ka ek foundational geometry chapter hai jo line symmetry aur rotational symmetry dono concepts ko clearly explain karta hai. Regular polygons ki lines of symmetry unke sides ke barabar hoti hain, circle ki infinite hoti hain, aur rotational symmetry ka order 360° ke andar total matches count karke nikala jaata hai.
Yeh chapter visual learning pe based hai — squared paper pe figures complete karna, real objects me symmetry dhoondhna, aur alphabets ko analyze karna. Practice ke liye Class 6 Maths chapter 9 Symmetry lines of symmetry worksheet jaise resources use karke concept ko strong kiya ja sakta hai, jo NCERT Class 6 Maths PDF download 2026-27 ke saath free available hain.
Symmetry ka concept isolated nahi hai — is chapter ka geometric foundation aage Class 6 Maths Lines and Angles types of angles notes aur Class 6 Maths chapter 8 Playing with Constructions compass ruler steps me directly use hota hai, jahan symmetric figures ko accurately construct karna sikhaya jaata hai.
In-Text Questions — Solutions
Kya sabhi triangles me line symmetry hoti hai?
Nahi. Sirf equilateral triangle (3 lines) aur isosceles triangle (1 line, sirf tab jab woh equilateral na ho) me line symmetry hoti hai. Ek scalene triangle (jiske teeno sides different length ke hon) me koi bhi line of symmetry nahi hoti, kyunki koi bhi fold uske do halves ko exactly match nahi karwa sakta.
Ek figure me kitni lines of symmetry ho sakti hain — kya limit hai?
Kam se kam 0 (jaise scalene triangle ya letter 'F' — no symmetry) se lekar infinite tak ho sakti hain (jaise circle, jiska har diameter ek line of symmetry hoti hai). Regular polygons ki lines of symmetry unke sides ke barabar hoti hain — jitne zyada sides, utni zyada lines of symmetry.
Rotational symmetry ka order kaise nikalte hain practically?
Ek asaan tarika hai: figure ko tracing paper pe copy karo, ek pin se center pe fix karo, aur dheere-dheere 360° tak rotate karo. Jitni baar (360° poora hone tak) figure exactly original shape jaisi wapas dikhe, wahi order of rotational symmetry hai. Har regular polygon ka order uske sides ke barabar hota hai — jaise regular hexagon ka order 6.
Exercise Questions — Solutions (Q1–Q6)
Draw the following shapes and mark all the lines of symmetry on them: (a) An equilateral triangle (b) A square (c) A regular pentagon
Step 1: Sabhi regular polygons me lines of symmetry ki sankhya sides ke barabar hoti hai.
(a) Equilateral triangle → 3 lines of symmetry (har vertex se opposite side ke midpoint tak)
(b) Square → 4 lines of symmetry (2 diagonals + 2 lines joining midpoints of opposite sides)
(c) Regular pentagon → 5 lines of symmetry (har vertex se opposite side ke midpoint tak)
Marking scheme: Correct figure ½ mark + correct number of lines ½ mark + sahi position ½ mark, har part ke liye.
Copy the given figure on a squared paper and complete it so that the resulting figure is symmetric about the given mirror line (assume a simple 'L' shaped half-figure with the mirror line along one edge).
Step 1: Har point ki mirror line se perpendicular distance measure karo (squares count karke).
Step 2: Mirror line ke doosri taraf same perpendicular distance pe corresponding point mark karo.
Step 3: Sabhi corresponding points ko usi tarah joh do jaise original figure me jude the (order reverse hoga, mirror image ki tarah).
Result: Poori figure ab mirror line ke around symmetric ban jaati hai — dono halves ek doosre ki exact mirror image hain.
State whether the following statements are True or False: (a) A circle has only one line of symmetry. (b) A rectangle (non-square) has 4 lines of symmetry. (c) A regular hexagon has 6 lines of symmetry. (d) An isosceles triangle (non-equilateral) has exactly 1 line of symmetry.
(a) False — circle ki infinite lines of symmetry hoti hain (koi bhi diameter ek line of symmetry hai).
(b) False — rectangle (jo square nahi hai) ki sirf 2 lines of symmetry hoti hain (dono opposite sides ke midpoints ko jodne wali lines).
(c) True — regular hexagon ki 6 lines of symmetry hoti hain (sides = lines of symmetry).
(d) True — isosceles triangle (jisme sirf do sides equal hain) ki exactly 1 line of symmetry hoti hai, jo base ke perpendicular bisector se guzarti hai apex se hoke.
Find the order of rotational symmetry for: (a) a square (b) an equilateral triangle (c) a regular hexagon (d) letter 'S'
Concept: Order of rotational symmetry = kitni baar 360° ke andar figure apne aap jaisi dikhti hai (including full 360°).
(a) Square → order 4 (rotation of 90°, 180°, 270°, 360° pe match karta hai)
(b) Equilateral triangle → order 3 (120°, 240°, 360°)
(c) Regular hexagon → order 6 (60°, 120°, 180°, 240°, 300°, 360°)
(d) Letter 'S' → order 2 (180° pe match karta hai, aur 360° pe)
Which of the following letters of the English alphabet have both line symmetry and rotational symmetry: H, O, X, Z, N?
Step 1: Har letter ko line symmetry ke liye check karo (kya koi mirror line hai jispe fold karke dono halves match ho jayein).
Step 2: Fir rotational symmetry check karo (kya 360° se kam rotation pe wapas same dikhta hai).
H: Line symmetry hai (vertical aur horizontal dono), rotational symmetry order 2 bhi hai → dono hain
O: Line symmetry (multiple lines) aur rotational symmetry (infinite/high order, circle jaisa) → dono hain
X: Line symmetry (vertical, horizontal, dono diagonals) aur rotational order 4 → dono hain
Z: Line symmetry nahi hai, par rotational symmetry order 2 hai → sirf rotational
N: Line symmetry nahi hai, par rotational symmetry order 2 hai → sirf rotational
Answer: H, O, X — inme dono types ki symmetry hain.
A photograph is reflected in a mirror placed vertically along its right edge. If a point in the photograph is 6 cm from the mirror line, how far will its image be from the same point (i.e., what is the total distance between the object point and its image)?
Step 1: Reflection ka basic rule: object aur image dono mirror line se equal perpendicular distance pe hote hain, opposite sides pe.
Object ki distance mirror line se = 6 cm
Image ki distance mirror line se = 6 cm (opposite side pe)
Step 2: Total distance between object point and image point = 6 cm + 6 cm
Total distance = 12 cm
Answer: 12 cm — kyunki mirror line hamesha object aur uski image ke beech ke line segment ka perpendicular bisector hota hai.
Important Equations — Ek Nazar Me
| Concept | Rule / Formula | Example |
|---|---|---|
| Line of symmetry | Ek line jo figure ko do exact mirror-image halves me baante | Square: 4 lines |
| Regular polygon lines of symmetry | Lines of symmetry = number of sides | Pentagon (5 sides) → 5 lines |
| Circle lines of symmetry | Infinite (har diameter ek line of symmetry) | Koi bhi diameter |
| Order of rotational symmetry | Total matches (including 360°) jab figure ko 360° tak rotate karein | Square → order 4 (90°, 180°, 270°, 360°) |
| Minimum rotation angle | 360° ÷ order of rotational symmetry | Hexagon: 360°÷6 = 60° |
| Reflection distance rule | Object aur image, mirror line se equal perpendicular distance pe hote hain | Object 6 cm door → image bhi 6 cm door, opposite side |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Rectangle (non-square) ki 4 lines of symmetry maan lena — asal me sirf 2 hoti hain, kyunki dono diagonals lines of symmetry nahi hoti (jab tak woh square na ho).
- Scalene triangle ya irregular quadrilateral me bhi symmetry dhoondhne ki koshish karna — kai shapes me bilkul bhi line of symmetry nahi hoti, aur yeh accept karna zaroori hai.
- Rotational symmetry ke order ko count karte waqt 360° (full rotation, jo hamesha match karega) ko count karna bhool jaana — order me yeh bhi shaamil hota hai.
- Mirror line ko hamesha vertical ya horizontal hi maan lena — mirror line diagonal ya kisi bhi angle pe ho sakti hai.
- Reflection ke figure complete karte waqt perpendicular distance ki jagah galat (angled) distance measure kar lena, jisse image asymmetric ban jaata hai.
- Letters jaise Z, N, S ko bina check kiye line symmetry wala maan lena — inme sirf rotational symmetry hoti hai, line symmetry nahi.
Board-Style Important Questions
- Draw all lines of symmetry for a given regular polygon (triangle/square/pentagon/hexagon) and state their count.
- Complete a given half-figure on squared/dot paper to make it symmetric about a marked mirror line.
- Identify and mark lines of symmetry in given alphabets, rangoli patterns, or real-life images.
- State the order of rotational symmetry for given geometric shapes (square, rectangle, equilateral triangle, regular hexagon).
- True/False or MCQ based statements testing understanding of line symmetry vs rotational symmetry differences.
- Given an object's distance from a mirror line, find the distance between the object and its reflected image.
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths chapter 9 Symmetry me kya-kya topics cover hote hain?
Ganita Prakash Class 6 ke Symmetry chapter me line symmetry (reflection symmetry), multiple lines of symmetry wale regular shapes, rotational symmetry aur uska order, aur real-life objects (rangoli, leaves, letters, traffic signs) me symmetry identify karna cover hota hai. Yeh chapter geometric intuition build karta hai jo aage Lines and Angles aur Playing with Constructions chapters me bhi kaam aata hai.
Line symmetry aur rotational symmetry me kya farak hai?
Line symmetry (jise reflection symmetry bhi kehte hain) tab hoti hai jab kisi figure ko ek line ke around fold karne se dono halves exactly match ho jayein — jaise square ya butterfly. Rotational symmetry tab hoti hai jab figure ko ek fixed point ke around 360° se kam angle pe ghumane par woh apne original shape jaisi dikhe — jaise pinwheel ya letter 'S'. Kuch shapes (square, circle) me dono types ki symmetry hoti hain, kuch me sirf ek.
Kaunsi shapes sabse zyada lines of symmetry rakhti hain?
Regular polygons me lines of symmetry ki sankhya unke sides ke barabar hoti hai — equilateral triangle me 3, square me 4, regular pentagon me 5, regular hexagon me 6. Circle sabse special hai kyunki uski infinite lines of symmetry hoti hain, kyunki har diameter ek line of symmetry hoti hai.
Symmetry chapter Class 6 exams ke liye kitna important hai aur kaise practice karein?
Symmetry ek high-scoring, visual chapter hai jisme practice se confidence jaldi aata hai. Squared paper (graph paper) pe half-figures complete karne ki practice zaroor karo, real objects (patte, rangoli patterns, alphabet letters) me symmetry dhoondo, aur mirror ka use karke reflection verify karo. Rotational symmetry ke liye tracing paper pe shape banakar rotate karke order count karna best tarika hai.
Symmetry ka concept Class 6 ke baad kahan use hota hai?
Symmetry ka concept aage Lines and Angles, Playing with Constructions (compass-ruler se symmetric figures banana), aur higher classes me coordinate geometry, mensuration (Perimeter and Area formulas symmetric shapes pe apply karte waqt), aur transformations (reflection, rotation) me directly use hota hai. Real world me bhi architecture, design, aur art me symmetry ka concept fundamental hai.
Ganita Prakash Class 6 Maths ki PDF kahan se milegi aur naya syllabus purane se kaise alag hai?
NCERT Class 6 Maths Ganita Prakash PDF official NCERT website (ncert.nic.in) se free download ki ja sakti hai 2026-27 session ke liye. Naya rationalised syllabus purani 14-chapter 'Mathematics' book se consolidate hokar 10 chapters ka ho gaya hai — isme negative numbers/integers (The Other Side of Zero) aur Goldbach's Conjecture jaisa unsolved-problems content (Prime Time chapter me) naye tarike se introduce hua hai jo pehle is level pe nahi tha.
Class 6 Maths — Saare Chapters
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