Lagnever AI English

Regular hexagon kaise banayein?

Short mein jawab

Regular hexagon apne centre pe milte chhe equilateral triangles se bana hota hai, kyunki chhe 60° angles ek bindu ke chaaron taraf ke 360° bhar dete hain. Isliye side jitne radius ka circle banaao, wahi radius circle pe chhe baar aage badhaao aur binduon ko jodo. Hexagon ka har angle 60° + 60° = 120° hai.

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Regular polygons

Regular polygon ki saari bhujaayein barabar aur saare angles barabar hote hain. Equilateral triangle aur square aise regular polygons hain jo tum pehle bana chuke ho. Barabar bhujaon waala pentagon ya hexagon compass se banaana aasaan hai, par uske angles shayad barabar na hon. Regular pentagon banaane ke liye wo vichaar chahiye jo tum aage padhoge; regular hexagon abhi ban sakta hai.

Ek bindu ke chaaron taraf chhe triangle

Regular hexagon ke aamne saamne ke konon ko jodo to centre pe milte chhe equilateral triangle dikhne ki ummeed hoti hai. Pakka karne ke liye sawaal ulta karo: kya chhe congruent equilateral triangle ek bindu ke chaaron taraf bina gap aur bina overlap fit ho sakte hain? Ek bindu ke chaaron taraf angles ka jod 360° hota hai. Jaise 40°, 60°, 50°, 30°, 40° aur 90° ka jod 310° hai, jo 50° ka gap chhodta hai, isliye wahan 70° ka angle fit nahi hoga. Equilateral triangles ke angles 60° hain, aur 6 × 60° = 360°, isliye chhe triangle theek fit hote hain.

Centre ke chaaron taraf chhe equilateral triangle regular hexagon banaate hain
Chhe triangle se hexagon

Unse bani figure ki chhe bhujaayein barabar hain, aur uska har angle do 60° angles se bana hai: 120°. Isliye ye regular hexagon hai. Iske lambe diagonals AD, BE aur CF seedhi lines hain, kyunki teen 60° angles ka jod 180° hai.

60° ka angle banaana

A se ek arc aur B se barabar arc C pe milte hain, jisse equilateral triangle aur 60° ka angle banta hai
Equilateral triangle se 60° ka angle

Segment AX pe A pe 60° banaane ke liye A centre lekar arc banaao jo AX ko B pe kaate. Usi radius se B se arc banaao jo pehle arc se C pe mile. Ab AB = AC (pehla arc) aur BC = AB (doosra arc), isliye triangle ABC equilateral hai aur ∠CAX = 60°. Seedhi line pe AC ki doosri taraf ka angle 180° − 60° = 120° hai, jo seedha hexagon ka angle deta hai.

Hexagon banaana

Sabse jaldi tareeka: jitni side chahiye, maan lo 4 cm ya 5 cm, utne radius ka circle banaao. Wahi khulaav rakhkar circle pe ek bindu lagao aur compass ko circle pe chhe baar aage badhaao, phir chhe binduon ko jodo. Har side radius ke barabar hai, kyunki har do padosi bindu centre ke saath equilateral triangle banaate hain. Ise har kone pe 120° angle aur chuni hui lambaai ki bhujaon se bhi bana sakte ho.

Jude hue constructions

60° bisect karne se 30°, aur 30° bisect karne se 15° milta hai. Angles jodne aur ghataane se aur bhi milte hain: 75° = 60° + 15°, 105° = 60° + 45° aur 135° = 90° + 45°. Regular hexagon ke ek chhod ek konon ko jodne se do equilateral triangle bante hain jo overlap karke 6-pointed star banaate hain. Star ke chhe point chhote equilateral triangle hain, kyunki har ek andar ke hexagon ke 120° angle ke bagal mein hai, jo seedhi line pe 60° chhodta hai.

Ruler aur compass se ban sakne waale angles
Ruler aur compass se angles

Ye kyun zaroori hai

Hexagon farsh ki tiles, bolt ke sir aur madhumakkhi ke chhatton mein dikhte hain, aur 60° ka angle in sabki chaabi hai. Buniyaadi tareeke geometric constructions kaise karein? mein dohraao, aur hexagon farsh kyun dhakte hain ye tiling patterns kya hain? mein dekho. Textbook ke sawaalon ke jawab Part 2 Chapter 6 ke NCERT solutions mein hain; poore Part 2 Chapter 6 ke notes dekho.

Practice karo

  1. Equilateral triangle ka har angle kitna hai?

    1. (a) 30°
    2. (b) 45°
    3. (c) 60°
    4. (d) 90°
    Jawab dekho

    Jawab: (c) 60°

  2. Ek bindu ke chaaron taraf 40°, 60°, 50°, 30°, 40° aur 90° ke angles rakhe hain. Gap kitna hai?

    1. (a) 40°
    2. (b) 50°
    3. (c) 60°
    4. (d) 70°
    Jawab dekho

    Jawab: (b) 50° Angles ka jod 310° hai, isliye gap 360° − 310° = 50° hai. 70° ka angle fit nahi hoga.

  3. Regular hexagon ki side 5 cm hai. Circle mein banaane ke liye compass ka radius kitna rakhoge?

    1. (a) 2.5 cm
    2. (b) 5 cm
    3. (c) 10 cm
    4. (d) 6 cm
    Jawab dekho

    Jawab: (b) 5 cm

  4. 15° ka angle kaise banaate hain?

    Jawab dekho

    Jawab: Equilateral triangle se 60° banaao, use bisect karke 30° pao, aur 30° ko bisect karke 15° pao.

  5. Regular hexagon mein bane star ke chhe point equilateral triangle kyun hain?

    Jawab dekho

    Jawab: Regular hexagon ka har angle 120° hai, isliye seedhi line pe uske bagal ka angle 60° hai. Har point triangle ke do angles 60° hain, aur teesra angle 180° − 120° = 60° hai. Teeno angles 60° hain, isliye wo equilateral hai.

Students ke sawal

4 cm side ka regular hexagon kaise banaate hain?

4 cm radius ka circle banaao. Compass 4 cm pe hi rakhkar circle pe ek bindu lagao aur circle pe aage badhte hue chhe bindu lagao. Unhe kram se jodo. Har side radius ke barabar hai, kyunki har do padosi bindu centre ke saath equilateral triangle banaate hain.

Ruler aur compass se 60° ka angle kaise banaate hain?

Line AX pe A pe 60° banaane ke liye A centre lekar arc banaao jo AX ko B pe kaate. Usi radius se B se arc banaao jo pehle arc se C pe mile. AC jodo. Triangle ABC mein AB = AC = BC hai, isliye wo equilateral hai aur ∠CAX = 60°.

Ek bindu ke chaaron taraf chhe equilateral triangle kyun fit hote hain?

Ek bindu ke chaaron taraf angles ka jod 360° hota hai. Har equilateral triangle ke angles 60° hain, aur 6 × 60° = 360°, isliye chhe triangle theek fit hote hain, bina gap aur bina overlap. Milkar wo regular hexagon banaate hain.

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