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Rotational Symmetry

Class 6 Maths · Chapter 9: Symmetry · NCERT Ganita Prakash section 9.2

Seekho

Tenzin 4 pankhudiyon wali kaagaz ki phirki banata hai. Wo use centre par pin karke dheere ghumaata hai. Chauthai chakkar (90°) ke baad wo bilkul shuru jaisi dikhti hai! 180°, 270° aur 360° par phir same dikhti hai.

Jo shape poore chakkar se kam ghumaane par same dikhe, usme rotational symmetry hai. Ek poore chakkar mein wo jitni baar same dikhe, wo uska rotational symmetry ka order hai. Phirki ka order 4 hai. Sabse chhota aisa ghumaav, yahan 90°, uska angle of symmetry hai.

360° ÷ 4 = 90°

Samabahu triangle 120°, 240° aur 360° par same dikhta hai: order 3. Regular hexagon: har 60° par, order 6. Rectangle: sirf aadhe chakkar par, order 2. Har shape ke liye order × angle of symmetry = 360°.

Har shape poore 360° ke chakkar ke baad same dikhti hai. Agar sirf tabhi, to shape mein rotational symmetry nahi. Teer ya patang mein line of symmetry hai par rotational symmetry nahi.

Ulta bhi hota hai: phirki aur parallelogram mein rotational symmetry hai par koi line of symmetry nahi. Letters S, N aur Z ulte bhi same dikhte hain (order 2), par koi mirror line kaam nahi karti.

Explore: har shape ghumao aur dekho kab wo phir apni outline mein fit hoti hai.

  1. Square ko tab tak ghumao jab tak wo shuru jaisa na dikhe.
  2. Ab 3 pankhudi wali phirki.
  3. Regular hexagon ke liye sabse chhota ghumaav dhoondo jo kaam kare.
  4. Rectangle ko tab tak ghumao jab tak same dikhe.

Yaad rakho

  • Rotational symmetry: shape poore chakkar se kam ghumaane par same dikhti hai.
  • Order = poore chakkar mein kitni baar same dikhe; angle of symmetry = 360° ÷ order.

Quick check

Ek shape 72°, 144°, 216°, 288° aur 360° ghumaane par same dikhti hai. Uska rotational symmetry order kya hai?

  1. 5
  2. 72
  3. 4
  4. 360
Answer

5. Ek poore chakkar mein 5 baar same dikhti hai: 360 ÷ 72 = 5.

Socho

Kya kisi shape ka angle of symmetry 50° ho sakta hai? Aur 45°?

Ek answer

45° chalta hai: regular octagon poore chakkar mein 8 baar same dikhta hai, aur 8 × 45° = 360°. 50° nahi, kyunki 360, 50 ka multiple nahi, to shape poore steps ke baad shuruaat par wapas nahi aayegi.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.