Parallel aur perpendicular lines
Short mein jawab
Perpendicular lines samkon, yaani 90°, pe milti hain; kaatne ki jagah chaaron angles barabar hon to har ek 90° hai. Parallel lines ek hi satah pe hoti hain aur kitna bhi badhaane pe nahi miltin. Parallel lines pe ek jaise teer aur samkon pe chhota square banaate hain, aur parallel lines set square se ya kaagaz modkar ban sakti hain.
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Perpendicular lines
Kya aisi do kaatti lines kheench sakte ho jinke chaaron angles barabar hon? Kaatne ki jagah ke chaaron angles ka jod 360° hai, isliye barabar hon to har ek 90°, yaani samkon, hoga. Samkon pe kaatne waali lines ek doosre ke perpendicular hain. Kone pe chhota square samkon dikhaata hai. Perpendicular lines ka khada aur leta hona zaroori nahi; kisi bhi tirchhi jodi ko perpendicular kahenge agar ve 90° pe milein.
Parallel lines
Alag-alag dishaon mein kheenche line segments dekho. Kuch badhaane pe saaf mil jaayenge; kuch, jo ek hi doori pe chalte hain, kabhi milte nahi lagte. Railway ki patriyan, copy ki lines, piano ki keys aur zebra crossing ki pattiyan roz ke udaaharan hain. Parallel lines ek hi satah ki ve lines hain jo dono taraf kitna bhi badhaane pe nahi miltin. Kala aur shading mein bhi parallel lines khoob use hoti hain.
Satah zaroori hai. Table pe aur board pe kheenchi lines kabhi na milein, phir bhi ve alag satahon pe hain, isliye parallel nahi hain.
Kaunsi lines parallel hain?
Dot paper pe jo lines dots ke beech ek jaise kadam leti hain, ve parallel hain. Figure 5.6 mein khadi lines a, h aur i parallel hain; leti lines c aur g parallel hain; d aur f, jo daayein neeche jhukti hain, parallel hain; aur b aur e, jo daayein upar jaati hain, parallel hain.
Kaagaz modkar parallel aur perpendicular lines
Ek chaukor kaagaz lo, jaise akhbaar ka panna. Iske aamne-saamne ke kinaare parallel hain, aur padosi kinaare perpendicular: ek bindu pe milte hain aur samkon banaate hain. Use leta aadha modo: tah upar aur neeche ke kinaaron ke parallel aur khade kinaaron ke perpendicular nayi line hai, yaani 3 parallel lines. Mude kaagaz ko phir modo to 5; ek baar aur to 9. Har tah pattiyan doguni karti hai, isliye n tahein 2ⁿ + 1 parallel lines deti hain. Khadi tah saari leti lines ke perpendicular hai, aur diagonal ke parallel tah bhi banaai ja sakti hai.
Parallel aur perpendicular ke nishaan
Chitron mein parallel lines ke ek set ki har line pe teer ka nishaan (>) banaate hain. Parallel lines ke doosre set pe do teer, teesre pe teen, waghera. Perpendicular lines ke beech samkon ko chhote square se dikhaate hain.
Parallel lines banaana
Dot paper pe leti ya khadi lines ke parallel banaana aasaan hai, par tirchhi lines ke liye mushkil, aur aankh dhokha kha sakti hai. Set square se ye pakka ho jaata hai. Ek line l kheencho aur set square ko uske saath khiskaate hue uske kinaare se do lines kheencho: dono l ke saath 90° banaati hain, isliye parallel hain. Bindu A se l ke parallel line ke liye, set square ka ek kinaara l pe rakho, doosre kinaare se ruler sataao, set square ko ruler ke saath tab tak khisko jab tak kinaara A tak na pahunche, aur us kinaare se line kheencho.
Kaagaz modna bhi kaam karta hai. Tah l ke perpendicular aisi tah t banao jo A se guzre, phir A se guzarti t ke perpendicular tah m banao. Lines l aur m dono t ke saath 90° banaati hain, isliye m, l ke parallel hai.
Ye kyun zaroori hai
Parallel aur perpendicular lines har jagah hain, sadkon aur imaaraton se lekar copy aur tiles tak. Barabar angles ka matlab parallel lines kyun hai, ye transversal ke angles mein hai, aur do kaatti lines ke angles linear pair aur vertically opposite angles mein. Har sawaal ke jawaab Chapter 5 ke NCERT solutions mein hain; poore Chapter 5 ke notes bhi dekho.
Practice karo
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Kaunsi jodi perpendicular hai?
Jawab dekho
Jawab: (b) Panne ke do kinaare jo kone pe milte hain
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Chaukor kaagaz ko do baar leta aadha moda gaya. Kinaare milaakar kitni parallel lines hain?
Jawab dekho
Jawab: (c) 5
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Kaatne ki jagah chhota square kya dikhaata hai?
Jawab dekho
Jawab: (b) Lines perpendicular hain
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Ruler aur set square se bindu A se hokar l ke parallel line kaise banaoge?
Jawab dekho
Jawab: Set square ka ek kinaara l pe rakho aur doosre kinaare se ruler kaskar sataao. Set square ko ruler ke saath tab tak khisko jab tak pehla kinaara A se na guzre, phir us kinaare se line kheencho. Nayi line l ke parallel hai.
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Ek teesri line ke perpendicular do lines aapas mein parallel kyun hoti hain?
Jawab dekho
Jawab: Teesri line ko transversal maano: dono lines uske saath 90° banaati hain, isliye ek corresponding jodi barabar hai, dono 90°. Barabar corresponding angles ka matlab hai ki dono lines parallel hain.
Students ke sawal
Perpendicular lines kya hain?
Perpendicular lines do lines hain jo samkon, 90°, pe milti hain. Kaatne pe chaaron angles barabar hote hain, aur kyunki milkar 360° hote hain, har ek 90° hai. Panne ya table ke padosi kinaare perpendicular hain, aur dikhaane ke liye kone pe chhota square banaate hain.
Parallel lines kya hain?
Parallel lines ek hi satah ki ve lines hain jo dono taraf kitna bhi badhaane pe nahi miltin, jaise railway ki patriyan ya copy ki lines. Jo lines kabhi nahi miltin par alag satahon pe hain, jaise ek table pe aur ek board pe, unhe parallel nahi kehte.
Kaagaz modkar parallel lines kaise milti hain?
Chaukor kaagaz ko leta aadha modo: tah upar aur neeche ke kinaaron ke parallel hai, yaani 3 parallel lines. Har agli tah pattiyan doguni karti hai, isliye n tahon ke baad 2ⁿ + 1 parallel lines: 3, 5, 9 waghera. Khadi tah in sabke perpendicular hai.
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