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Class 7 Maths Part 2 Chapter 6: Constructions and Tilings (Hinglish Notes)

Ye chapter 5 lines mein

Constructions and Tilings ke do hisse hain. Constructions mein sirf bina nishaan waale ruler aur compass se perpendicular bisector, 90°, 45° aur 60° ke angle, angle bisector, angle ki copy, parallel lines aur regular hexagon banaate hain, aur congruent triangles batate hain ki har tareeka kyun chalta hai. Tiling mein shapes se jagah bina gap aur bina overlap dhakte hain, tangram se grid aur poore plane tak.

Part 2 Chapter 6 ka mind map: perpendicular bisector, right angle aur parallel lines, angle bisection, 60° aur regular hexagon, designs, aur tiling
Poora chapter ek page pe

Ye chapter kis baare mein hai?

Class 6 mein tumne do arcs se aankh banaayi thi, compass kahan rakhna hai iska andaaza lagaakar. Ye chapter dikhata hai ki aise bindu sirf bina nishaan waale ruler aur compass se theek theek kaise nikaalein, aur Geometric Twins chapter ke congruent triangles se ye bhi ki har tareeka kyun chalta hai. Iska doosra hissa tiling ke baare mein hai: kisi shape ko tukdon se aise dhakna ki kuch bacha na rahe aur kuch ek doosre pe na chadhe.

Perpendicular bisector

X aur Y se arcs A aur B pe milte hain; AB, XY ka perpendicular bisector hai
XY ka perpendicular bisector

Segment XY ke upar aur neeche X se aur Y se ek hi radius ke arcs banaao. Wo A aur B pe milte hain, aur line AB, XY ke beech ke bindu se right angle pe guzarti hai: ye perpendicular bisector hai. Kyun? SSS se ΔABX ≅ ΔABY, isliye A pe dono angles barabar; phir SAS se ΔAOX ≅ ΔAOY, isliye OX = OY aur O pe dono angles barabar, har ek 180° ka aadha, yaani 90°. X aur Y se barabar door har bindu isi line pe hota hai. Aur padho geometric constructions kaise karein? mein.

Angles aur parallel lines

Line ke bindu O pe 90° banaane ke liye O se barabar door X aur Y lagao aur dono se barabar door ek aur bindu dhoondho. Angle ko barabar arcs se bisect karo: O se arms pe A aur B tak, phir A aur B se milne ke bindu C tak; OC angle ko aadha karta hai, to 90° se 45° banta hai. Compass se ek arc aur ek chord le jaakar angle copy hota hai, aur transversal jo angle line ke saath banata hai use copy karne se parallel line milti hai. Puraane Sulba-Sutras yahi kaam ek rassi aur do khoontiyon se karte the.

Barabar arcs se angle bisect karna: OC angle XOY ko do barabar angles mein baantta hai
Angle bisect karna

60° angle aur regular hexagon

A se ek arc aur B se usi radius ka arc C pe milte hain, aur ABC equilateral triangle banta hai, isliye ∠CAB 60° hai. Aise chhe triangle ek bindu ke chaaron taraf theek fit hote hain, kyunki 6 × 60° = 360°, aur milkar regular hexagon banaate hain jiske har angle 120° ke hain. 60° ko bisect karne se 30° aur phir 15° milte hain. Dekho regular hexagon kaise banayein?

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

Tiling

Ek square se kaate gaye saat tangram tukdon ko jodkar teer, jaanwar aur akshar ban sakte hain. Grid ko 2 × 1 tiles se tabhi dhak sakte hain jab usme squares ki ginti even ho, aur chessboard ki tarah rangne se aur pata chalta hai: har tile ek kaala aur ek safed square dhakta hai, isliye dono rang barabar hone chahiye. Regular polygons mein sirf equilateral triangle, square aur regular hexagon poora plane dhakte hain, isiliye madhumakkhiyan hexagon ke khaane banaati hain. Padho tiling patterns kya hain? Har sawaal ka jawab, tangram figures aur tiling paheliyon samet, Part 2 Chapter 6 ke NCERT solutions mein hai.

Key terms (zaroori shabd)

TermMatlab
BisectionKisi line segment, angle ya figure ko do ek jaise hisson mein baantna.
Perpendicular bisectorWo line jo segment ko do barabar hisson mein kaatti hai aur us pe perpendicular hoti hai. Is line ka har bindu segment ke dono siron se barabar door hota hai.
Angle bisectorWo ray jo angle ko do barabar angles mein baantti hai. Ise barabar arcs aur congruent triangles se nikaalte hain.
Ruler aur compass constructionSirf bina nishaan waale ruler (seedhi lines ke liye) aur compass (gol, arcs aur lambaai copy karne ke liye) se, bina naape, figure banaana.
SSS aur SAS congruenceDo triangles congruent hain agar teeno bhujaayein milein (SSS), ya do bhujaayein aur unke beech ka angle milein (SAS). Zyaadatar constructions isi se saabit hote hain.
TransversalWo line jo do ya zyaada lines ko kaatti hai. B se guzarti line m ke parallel hai agar wo transversal ke saath wahi corresponding angle banaaye.
Regular polygonAisa polygon jiski saari bhujaayein barabar aur saare angles barabar hon, jaise equilateral triangle, square ya regular hexagon.
Regular hexagonChhe bhujaon waala regular polygon. Ye apne centre ke chaaron taraf chhe equilateral triangles se bana hota hai, aur iska har angle 120° hai.
TangramChina mein shuru hui paheli: ek square ke 7 tukde (2 bade, 1 medium aur 2 chhote triangle, ek square aur ek parallelogram), jinhe jodkar figures banaate hain.
TilingKisi jagah, ya poore plane, ko shapes se aise dhakna ki na koi gap rahe na koi overlap.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. Is chapter ke constructions mein kaun se auzaar use hote hain?

    1. (a) Protractor aur ruler
    2. (b) Bina nishaan ka ruler aur compass
    3. (c) Set square aur protractor
    4. (d) Sirf nishaan waala scale
    Jawab dekho

    Jawab: (b) Bina nishaan ka ruler aur compass

  2. 60° angle ko bisect karne pe kya milta hai?

    1. (a) 120°
    2. (b) 45°
    3. (c) 30°
    4. (d) 15°
    Jawab dekho

    Jawab: (c) 30°

  3. Regular hexagon ka har angle kitna hai?

    1. (a) 60°
    2. (b) 90°
    3. (c) 108°
    4. (d) 120°
    Jawab dekho

    Jawab: (d) 120°

  4. Kya 5 × 7 grid ko 2 × 1 tiles se dhak sakte hain?

    1. (a) Haan
    2. (b) Nahi, kyunki 35 odd hai
    3. (c) Sirf ek square hataane pe
    4. (d) Sirf tiles na ghumaane pe
    Jawab dekho

    Jawab: (b) Nahi, kyunki 35 odd hai

  5. Kaunsa regular polygon akele plane nahi dhak sakta?

    1. (a) Equilateral triangle
    2. (b) Square
    3. (c) Regular pentagon
    4. (d) Regular hexagon
    Jawab dekho

    Jawab: (c) Regular pentagon

  6. Tangram mein kitne tukde hote hain?

    1. (a) 5
    2. (b) 6
    3. (c) 7
    4. (d) 8
    Jawab dekho

    Jawab: (c) 7

Students ke sawal

Class 7 Maths Part 2 Chapter 6 ke main topics kya hain?

Ruler aur compass se geometric constructions: perpendicular bisector, bindu pe 90° angle, angle bisection, angle ki copy, parallel lines, arches, 60° angle aur regular hexagon, congruent triangles se saboot aur Sulba-Sutras ke rassi ke tareekon ke saath; aur tiling: tangram, 2 × 1 tiles se grid dhakna, chessboard rang ki chaal aur poora plane dhakna.

Kya Constructions and Tilings nayi Ganita Prakash Part 2 book mein hai?

Haan. Ye Ganita Prakash, Class 7 Maths textbook Part 2 (2026-27) ka Chapter 6 hai, pages 136 se 163 tak. Ye Part 2 ke chapter Geometric Twins ke baad aata hai, jahan congruent triangles padhaaye gaye.

Sirf ruler aur compass se hi construction kyun karte hain?

Kyunki ye sabse saral auzaar sateek nateeja dete hain. Compass lambaai theek theek copy karta hai aur arcs banata hai, aur ruler binduon ko jodta hai, isliye figures tark se sahi hoti hain, naap se nahi. Perpendicular bisector se beech ka bindu nikaalna nishaan waale scale se naapne se zyaada sateek hai.

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