Class 6 Maths · Chapter 8
Short answer:
Chapter 8 Playing with Constructions Class 6 Maths Ganita Prakash me sikhata hai ki sirf ruler aur compasses (parkar) se — bina protractor ke — geometric shapes precisely kaise banayi jaati hain. Perpendicular bisector, angle bisection, 60°/30° angles, equilateral triangle aur circle ki construction — sab step-by-step solutions yahan diye gaye hain.
Chapter 8 "Playing with Constructions" Class 6 Maths Ganita Prakash ka wo chapter hai jahan bachche pehli baar formal geometric constructions se milte hain — sirf ruler aur compasses (parkar) ka use karke, bina protractor ke. Ye chapter Chapter 7 "A Peek Beyond the Point" (basic geometry — points, lines, angles) ka natural extension hai, aur aage Class 6 ke hi Chapter 9 "Symmetry" ke saath bhi conceptually connect hota hai kyunki dono me precise, systematic hand-drawing skill chahiye hota hai.
Is chapter ki khaasiyat ye hai ki ye students ko "measure karo" se "construct karo" ki taraf le jaata hai — matlab angle ko protractor se naapne ke bajaye, geometric logic (jaise equilateral triangle ki property) use karke exactly banana. Ye skill Class 9-10 ki construction chapters (jahan triangles, tangents wagalah construct karte hain) ki neev banti hai.
Chapter 8 Summary — 5 Minute Revision
Chapter 8 "Playing with Constructions" Class 6 Maths Ganita Prakash ka geometry-practical chapter hai jisme sirf ruler aur compasses se — bina protractor use kiye — precise geometric figures banana seekhte hain. Core constructions hain: line segment ko copy karna, perpendicular bisector banana (jahan har point dono endpoints se equidistant hota hai), 60° angle equilateral triangle property se construct karna, uske bisection se 30° nikalna, 60°+30° combine karke 90° banana, aur equilateral triangle construct karna. Har construction ka exam me marking arcs/marks visible chhodna zaroori hota hai kyunki wahi construction ki authenticity prove karte hain. Ye chapter Chapter 7 "A Peek Beyond the Point" ke basic geometry concepts ko aage badhata hai aur Chapter 9 "Symmetry" ke precise-drawing skills se bhi connect hota hai. Class 6 Maths ka poora syllabus — Chapter 1 "Patterns in Mathematics", Chapter 2 "Lines and Angles", Chapter 5 "Prime Time" (jisme Goldbach's Conjecture jaisa naya unsolved-problems content hai), Chapter 4 "The Other Side of Zero" (negative numbers/integers), aur "Data Handling and Presentation" (bar graph, pictograph) — sab NEP-aligned 10-chapter rationalised structure ka hissa hain jo purani 14-chapter Mathematics textbook se consolidate hua hai.
In-Text Questions — Solutions
Ruler aur compasses se construction karne ka main advantage kya hai protractor ke comparison me?
Ruler-compass constructions mathematically exact hote hain — protractor ki reading me chhoti-chhoti human error ho sakti hai (jaise 59° ya 61° padh lena), lekin geometric construction method se angle exactly 60° banta hai bina kisi measurement error ke, kyunki ye equilateral triangle jaisi geometric properties par based hota hai.Ek line segment ki perpendicular bisector par koi bhi point kis property ko satisfy karta hai?
Perpendicular bisector par jo bhi point ho, wo dono endpoints A aur B se equal distance (equidistant) par hota hai. Yani agar P bisector par hai, to PA = PB hamesha true hoga — ye hi construction ka core logic bhi hai.Exercise Questions — Solutions (Q1–Q6)
8.1 (a) Draw a line segment AB of length 7.3 cm and construct its perpendicular bisector using ruler and compasses.
Steps:
- Draw AB = 7.3 cm using ruler.
- Compass ko AB ki aadhi length se zyada (jaise 5 cm) kholo. A se center rakh kar upar aur neeche arcs banao.
- Same radius rakh kar B se center rakh kar phir do arcs banao jo pehle wale arcs ko P aur Q par kaatein.
- P aur Q ko milao — ye seedhi rekha PQ, AB ki perpendicular bisector hai, jo AB ko M par 90° par bisect karti hai.
AM = MB = 3.65 cm, angle PMB = 90°
8.1 (b) Construct the perpendicular bisector of a line segment PQ = 5.8 cm and verify by folding the paper.
Same method: PQ = 5.8 cm draw karo, dono ends se equal radius (>2.9 cm) ke arcs upar-neeche banao, unke intersection points ko milao. Verification: paper ko bisector line ke saath fold karo — point P point Q par exactly overlap hona chahiye, jo confirm karta hai ki construction sahi hai.
8.2 Construct an angle of 60° using ruler and compasses, without using a protractor.
Steps:
- Ray OA draw karo.
- O ko center rakh kar koi bhi radius se arc banao jo OA ko point B par kaate.
- Same radius rakh kar B ko center rakh kar ek aur arc banao jo pehle arc ko C par kaate.
- O se hote hue C tak ray draw karo.
Angle AOC = 60° (kyunki triangle OBC equilateral banta hai, isliye har angle 60°)
8.3 Using the 60° construction, construct a 30° angle by bisecting it.
Pehle 60° angle construct karo (upar wali method se). Uske baad angle bisector banao: dono arms par ek-ek point mark karke same radius se do arcs banao jo ek dusre ko andar kaatein, us intersection point ko vertex O se milao.
Resulting angle = 60° ÷ 2 = 30°
8.4 Construct an equilateral triangle with side 6 cm using only ruler and compasses.
Steps:
- Base AB = 6 cm draw karo.
- A ko center rakh kar 6 cm radius se arc banao.
- B ko center rakh kar 6 cm radius se doosra arc banao — dono arcs point C par kaatenge.
- A-C aur B-C milao.
Triangle ABC equilateral hai kyunki teeno sides 6 cm equal hain, aur har angle 60° hoga.
8.5 Draw a circle of radius 4 cm and construct two radii that are perpendicular to each other.
Compass ko 4 cm kholo, kisi bhi center O se circle draw karo. O se ek radius OA kheecho. Phir OA par 90° ka angle construct karo (60° + 30° combine karke, ya diameter draw karke us par perpendicular bisector construct karke) taaki dusra radius OB, OA ke perpendicular ban jaye.
Angle AOB = 90°, OA = OB = 4 cm (radius)
Important Equations — Ek Nazar Me
| Construction | Rule / Steps |
|---|---|
| Perpendicular Bisector of AB | Radius > half of AB, dono ends se arcs banao, intersection points ko milao |
| 60° Angle | Ray se ek arc, us arc ke point se same radius ka doosra arc — vertex se naye point tak milao |
| 30° Angle | 60° angle ka bisector nikalo (30° = 60° ÷ 2) |
| 90° Angle | 60° + 30° combine karo, ya perpendicular bisector method se seedha 90° banao |
| 120° Angle | Do baar 60° construct karo ek hi base ray se lagatar |
| Equilateral Triangle (side a) | Base = a, dono ends se radius a ke arcs, intersection = third vertex |
| Angle Bisector | Vertex se arc jo dono arms ko kaate, un points se equal radius ke arcs jo andar kaatein — vertex se us point tak milao |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Compass ka radius construction ke beech me accidentally change ho jaana — isse arcs match nahi karte aur poori construction galat ho jaati hai. Compass ko lock karke fix radius par hold karo jab tak wo step complete na ho.
- Perpendicular bisector banate waqt radius AB ki aadhi length se kam le lena — isse dono taraf ke arcs intersect hi nahi karenge. Radius hamesha AB ki half length se zyada hona chahiye.
- 60° angle construct karte waqt dusra arc galat radius se banana — dono arcs (ray se aur pehle point se) ka radius EXACTLY same hona chahiye, tabhi equilateral triangle property apply hogi.
- Construction ke arcs ko erase kar dena final answer submit karne se pehle — CBSE marking scheme me construction ke visible arcs/marks hi ye prove karte hain ki answer sahi method se aaya hai, sirf final figure kaafi nahi hai.
- Angle bisector banate waqt dono arms par unequal distance par points mark karna — bisector arms ke equal distance wale points se hi accurately banti hai.
- Pencil ka sharp point use na karna aur compass ko loosely hold karna — isse lines thick ho jaati hain aur measurement me 1-2mm ka error aa jaata hai jo exam me marks kaat sakta hai.
Board-Style Important Questions
- Construct a line segment of given length and draw its perpendicular bisector using ruler and compasses only.
- Construct an angle of 60° at a given point on a ray, without using a protractor.
- Using compasses, construct a 90° angle and verify it using a set square or by paper folding.
- Construct an equilateral triangle when one side is given, and justify why all its angles are 60°.
- Bisect a given angle using ruler and compasses and describe each step clearly.
- Construct an angle of 120° at a point on a line using only ruler and compasses.
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths Chapter 8 Playing with Constructions me kya-kya seekhte hain?
Is chapter me ruler (scale) aur compasses ka use karke bina protractor ke geometric constructions karna seekhte hain — line segment banana aur copy karna, perpendicular bisector, angle bisector, 60°/30°/90°/120° jaise standard angles, aur equilateral triangle. Ye Ganita Prakash ka geometry-practical chapter hai jo hath se precise drawing ka skill develop karta hai.
Kya Chapter 8 me protractor allowed hai?
Nahi — is chapter ka core idea hi ye hai ki sirf ruler aur compasses (parkar) se constructions karna hai, protractor use nahi karna. Ye classical Euclidean construction method hai jisse angles bina measure kiye, sirf geometric logic se banaye jaate hain.
60° ka angle bina protractor ke kaise banate hain?
Ek ray draw karo, uske starting point O ko center bana kar koi bhi radius se arc kaato jo ray ko B par kaate. Fir wahi radius rakh kar B ko center bana kar doosra arc kaato jo pehle wale ko C par kaate. O se C tak line milao — angle AOC automatically 60° ban jaata hai kyunki triangle OBC equilateral hota hai.
NCERT Class 6 Maths Ganita Prakash PDF kahan se download karein 2026-27 session ke liye?
Official rationalised Ganita Prakash textbook PDF NCERT ki official website ncert.nic.in ke 'Publications' ya 'e-books' section se free download ho sakti hai. Third-party sites bhi PDF host karte hain lekin latest 2026-27 rationalised version ke liye official NCERT site sabse reliable source hai.
Class 6 Maths ka naya syllabus purane syllabus se kitna different hai?
Purani 'Mathematics' textbook 14 chapters ki thi; naya NEP-aligned 'Ganita Prakash' sirf 10 chapters me consolidate ho gaya hai. Isme negative numbers/integers (The Other Side of Zero) aur Goldbach's Conjecture jaisa unsolved-problems content (Prime Time chapter) naye tarike se introduce hua hai, aur data handling ka scope bhi expand hua hai.
Chapter 8 Playing with Constructions exam ke liye kitna important hai?
Ye ek practical-skill chapter hai jisme step-by-step construction accuracy check hoti hai — isliye scoring aasan hai agar steps sahi order me likhe jaayein aur diagram clean ho. Compass ka correct use aur arcs ka sahi radius maintain karna common exam requirement hota hai.
Class 6 Maths — Saare Chapters
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