Class 6 Maths Chapter 9: Symmetry (Hinglish Notes)
Ye chapter 5 lines mein
Kisi figure mein symmetry tab hoti hai jab uske kuch hisse ek tay pattern mein dohraaye jaate hain. Line of symmetry figure ko do aise hisson mein kaatti hai jo us line pe modne pe ekdum ek doosre pe aa jaate hain, aur ek figure mein aisi kai lines ho sakti hain. Figure mein rotational symmetry tab hoti hai jab wo ek fixed centre ke chaaron taraf 360° se kam ghumane pe bilkul waisi hi dikhe. Aisa angle, angle of symmetry hai, aur figure ke saare angles of symmetry sabse chhote angle ke multiples hote hain.
Symmetry kya hai?
Phool kai dishaon se ek jaisa dikhta hai, titli ke dono pankh mel khaate hain, aur rangoli ki pankhudiyan chauthai chakkar ghumane pe apni jagah wapas aa jaati hain. In sab mein figure ke hisse ek tay pattern mein dohraaye jaate hain. Yahi symmetry hai, aur aisi figures symmetrical kehlaati hain. Baadal mein aisa koi pattern nahi, isliye wo symmetrical nahi hai. Taj Mahal aur mandir ka gopuram bhi symmetrical hain: unke baayein aur daayein hisse mel khaate hain.
Lines of symmetry
Do barabar sides wale triangle ko uske upar ke kone aur base ke beech ke point se guzarti line pe modo, to ek hissa doosre ko poori tarah dhak leta hai: dono hisse mirror halves hain. Jo line figure ko aise do hisson mein kaate jo us line pe modne pe ekdum ek doosre pe aa jaayein, wo line of symmetry hai.
Figure mein ek se zyada lines bhi ho sakti hain. Square kaagaz ko khada, leta aur dono diagonals pe modne se dikhta hai ki square mein 4 lines of symmetry hain. Jo rectangle square nahi, usme sirf 2 hain: diagonal pe modne se hisse mel nahi khaate. Aur padho line of symmetry kya hai mein.
Reflection
Ye bhi keh sakte hain ki line of symmetry figure ke ek taraf ke hisse ko doosri taraf reflect karti hai. Square ke kono ko A, B, C aur D naam do. Khadi line of symmetry mein reflect karne pe A, B ki jagah aur D, C ki jagah chala jaata hai, aur ulta bhi. Jis figure mein line of symmetry ho, usme reflection symmetry bhi kehte hain.
Symmetric shapes banana
- Syahi ke dhabbe: mude kaagaz ke ek aadhe hisse pe syahi giraao, dono hisse dabaao aur kholo. Pattern mod ke dono taraf symmetric hota hai.
- Modna aur kaatna: mude kaagaz se koi shape kaato aur kholo. Mod cut-out ki line of symmetry hai. Patti ko kai baar mod ke kaatne se kai lines of symmetry wala dohraata design banta hai.
- Chhed karna: mude square mein ek chhed karke kholo to do chhed bante hain, mod ke dono taraf, usse barabar doori pe.
Rotational symmetry
Kaagaz ki windmill mein koi line of symmetry nahi hai, phir bhi wo apne centre ke point ke chaaron taraf 90° ghumane pe bilkul waisi hi dikhti hai. Usme rotational symmetry hai. Fixed point centre of rotation hai, aur jitna ghumane pe figure bilkul waisi dikhe, wo angle of symmetry hai. Windmill ke angles of symmetry 90°, 180°, 270° aur 360° hain. Har figure 360° ke baad apni jagah wapas aa jaati hai, isliye 360° hamesha angle of symmetry hai. Figure mein rotational symmetry tabhi hai jab 0° aur 360° ke beech bhi koi angle of symmetry ho. Aur padho rotational symmetry kya hai mein.
Angles of symmetry
Radial arms wali figure mein rotational symmetry tab hoti hai jab padosi arms ke beech ke angles barabar hon. 3 arms mein angle 360° ÷ 3 = 120° hona chahiye, jisse angles 120°, 240° aur 360° milte hain; 4 arms mein 90°, aur 5 arms mein 72°. 7 arms mein sabse chhota angle 360° ÷ 7 = 51 3/7° hai, jo poora number nahi. Har baar angles of symmetry sabse chhote angle ke multiples hote hain, aur sabse chhota angle poora number ho to wo 360 ka factor hota hai. Angles of symmetry ki ginti order of rotational symmetry kehlaati hai.
Circle ki symmetries
Circle sabse zyada symmetric shape hai. Use uske centre ke chaaron taraf kisi bhi angle se ghumao, wo apne aap pe aa jaata hai, isliye har angle angle of symmetry hai. Aur har diameter line of symmetry hai. Pahiye, pankhe aur kai phoolon mein bhi rotational symmetry hoti hai. Chapter ke har sawal ka jawab Chapter 9 ke NCERT solutions mein hai.
Key terms (zaroori shabd)
| Term | Matlab |
|---|---|
| Symmetry (samamiti) | Figure ke hisse jo ek tay pattern mein dohraaye jaate hain. Symmetry wali figure symmetrical kehlaati hai. |
| Line of symmetry (axis of symmetry) | Wo line jo figure ko do aise hisson mein kaate jo us line pe modne pe ekdum ek doosre pe aa jaayein. |
| Mirror halves | Line of symmetry ke dono taraf ke hisse; har ek doosre ka mirror image hai. |
| Reflection symmetry | Ek ya zyada lines of symmetry wali figure ki symmetry: line har taraf ko doosri taraf reflect karti hai. |
| Rotational symmetry | Figure mein ye tab hai jab wo 0° aur 360° ke beech ke kisi angle se ghumane pe bilkul waisi hi dikhe. |
| Centre of rotation | Wo fixed point jiske chaaron taraf figure ghumaayi jaati hai. |
| Angle of (rotational) symmetry | Wo angle jitna ghumane pe figure bilkul waisi hi dikhe. 360° hamesha ek angle of symmetry hai. |
| Order of rotational symmetry | Figure ke angles of symmetry ki ginti, 360° ko milakar. Windmill ka order 4 hai. |
| Radial arms | Centre se bahar ki taraf failti bhujaayein, jaise pahiye ki teeliyan ya pankhe ke blades. |
| Diameter (vyaas) | Circle ke centre se guzarti, ek kinaare se doosre kinaare tak ki line. Har diameter circle ki line of symmetry hai. |
| Asymmetrical | Jisme koi symmetry na ho, jaise baadal ki shape ya scalene triangle. |
Is chapter ke topics
Practice karo
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Square mein kitni lines of symmetry hoti hain?
Jawab dekho
Jawab: (c) 4
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Jo rectangle square nahi hai, uski line of symmetry inme se kaunsi nahi hai?
Jawab dekho
Jawab: (c) Diagonal Rectangle ko diagonal pe modne se dono hisse ekdum ek doosre pe nahi aate.
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Kaagaz ki windmill 90° ghumane pe waisi hi dikhti hai. Uske angles of symmetry kya hain?
Jawab dekho
Jawab: (c) 90°, 180°, 270° aur 360°
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Ek figure mein 5 barabar radial arms hain jinke beech barabar angles hain. Uska sabse chhota angle of symmetry kya hai?
Jawab dekho
Jawab: (c) 72° 360° ÷ 5 = 72°.
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Kaunsa kathan sahi hai?
Jawab dekho
Jawab: (b) Har figure ka 360° angle of symmetry hota hai
Students ke sawal
Class 6 Maths Chapter 9 mein kya padhte hain?
Symmetry kya hai, lines of symmetry, ek se zyada lines of symmetry wali figures, reflection, syahi ke dhabbe, modna, kaatna aur chhed karke symmetric shapes banana, rotational symmetry, centre aur angles of rotational symmetry, radial arms wali figures, aur circle ki symmetries.
Kya Symmetry nayi Ganita Prakash book mein hai?
Haan. Symmetry Ganita Prakash ka Chapter 9 hai, jo 2026-27 session mein Class 6 Maths ki textbook hai.
Line symmetry aur rotational symmetry mein kya fark hai?
Figure mein line symmetry tab hai jab ek line pe modne se dono hisse ekdum mel khaayein. Rotational symmetry tab hai jab ek fixed point ke chaaron taraf poore chakkar se kam ghumane pe wo bilkul waisi dikhe. Square mein dono hain; pinwheel mein sirf rotational symmetry hai.
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