Class 6 Maths Chapter 2: Lines and Angles (Hinglish Notes)

Point, line segment, line aur ray

Ye plane geometry ki neev hain. Point ek sateek jagah hai: tez pencil ya sui ki nok iska idea deti hai. Iski na lambaai, na chaudaai, na oonchaai hoti hai, aur capital letter se naam diya jaata hai, jaise point P.

Kaagaz modkar kholo: crease se line segment ka idea milta hai. Do points A aur B ke beech ke saare raaston mein sabse chhota line segment AB hai, jiske end points A aur B hain. Ise dono taraf hamesha ke liye badhaao to line AB banti hai, jise kabhi ek chhote letter jaise l se bhi bulaate hain. Ray ek point se shuru hokar ek disha mein hamesha chalti hai, jaise torch, lighthouse ya Suraj ki roshni. Ray AP, A se shuru hokar P se guzarti hai.

Ek point se jitni chaaho utni lines bana sakte ho, par do points se theek ek line guzarti hai. Aur padho: point, line segment aur ray mein fark.

Angles

Angle do rays se banta hai jinka starting point ek hi ho. ∠DBE mein rays BD aur BE arms hain aur B vertex hai. Vertex beech mein likhte hain: ∠DBE ya ∠EBD, ya bas ∠B jab koi confusion na ho.

Jaise-jaise Vidya apni kitaab ka cover aur kholti hai, angle badhta jaata hai. Angle ka size vertex ke chaaron or ek arm ko doosri arm tak le jaane ke liye zaroori ghumaav (rotation ya turn) hai. Compass, kainchi, chashma, batua aur dibbe ka dhakkan, sab ek arm ko doosri ke muqaable ghumaakar angle banaate hain. Aur padho: angle kya hai.

Angles ki tulna

Do angles ki tulna superimposition se hoti hai: ek ko doosre par aise rakho ki vertex saath hon aur ek arm doosri arm par. Agar baaki arms bhi mil jaayein, to angles barabar hain. Vertex par centre rakha ek paardarshi (transparent) gola bhi bina trace kiye tulna mein madad karta hai. ‘Rotating arms’ activity dikhaati hai ki angle ke aakaar ki khaali jagah (slit) se sirf wahi arms nikalti hain jinka angle bilkul utna ho, chahe unki lambaai kuch bhi ho.

Khaas angles

Jab Vidya kitaab mez par poori khol deti hai, cover aadha chakkar ghoomta hai aur uski arms ek seedhi line mein aa jaati hain: ye straight angle hai. Straight angle ko aise modo ki arms ek-doosre par aayein, to do barabar angles bante hain, har ek right angle: chauthaai chakkar, L ke aakaar ka. Right angle par milne waali lines perpendicular hoti hain. Right angle se chhote angles acute (nukeele) hain; right angle aur straight angle ke beech ke angles obtuse (bhothe) hain. Aur padho: angles ke types.

Degrees mein angle naapna

Mathematicians ne poore chakkar ko 360 barabar hisson mein baanta, har hissa 1 degree (1°). Yaani poora chakkar 360°, straight angle 180° aur right angle 90°. 360 ka number purana hai: Rigveda mein 360 aaron (spokes) waale pahiye ki baat hai, kai purane calendars mein 360 din the, aur 360, 7 ko chhodkar 1 se 10 tak har number se poora bant jaata hai.

Protractor aadhe gole par 180 barabar hisse dikhaata hai, har 10° par lamba aur har 5° par madhyam nishaan. Isme numbers ke do set hain, ek-ek har disha mein, taaki kisi bhi taraf ke 0 se shuru kar sako.

Kaagaz ka semicircle baar-baar aadha modkar apna protractor bhi bana sakte ho: crease 90°, phir 45° aur 135°, phir har 22.5° par nishaan dete hain. Kisi angle ko modkar aadha karna use bisect karna hai, aur crease angle bisector hai. ∠TIN = 30° banaane ke liye IN banao, protractor ka centre I par aur IN ko 0 par rakho, 30 par T lagao aur IT jodo. Aur padho: protractor se angle kaise naapein.

Angles ke types aur unke maap

Type	Maap
Acute	0° se zyaada aur 90° se kam
Right	theek 90°
Obtuse	90° se zyaada aur 180° se kam
Straight	theek 180°
Reflex	180° se zyaada aur 360° se kam
Poora chakkar	theek 360°

Hamaare aas-paas ke angles

Ghadi ki suiyaan, kabze par khulta darwaaza, peeche khincha jhoola aur slide ki dhalaan, sab angles banaate hain. Ghadi ke 12 nishaan 360° ko 30° ke hisson mein baantte hain, isliye 1 baje suiyon ke beech 30° aur 6 baje 180° hota hai. Ashoka Chakra ke 24 aare 15° ke gap banaate hain.

Har “Figure it Out” sawaal ka jawab Chapter 2 ke NCERT solutions mein hai.