Class 7 Maths Chapter 5: Parallel and Intersecting Lines (Hinglish Notes)

Ye chapter kis baare mein hai?

Ek chaukor kaagaz ko alag-alag tarah modo aur tahon pe line kheencho: bahut si lines ban jaati hain. Kuch jodiyan milti hain; kuch kaagaz ke baahar badhaane pe bhi milti nahi lagtin. Ye chapter samtal satah, jaise table, panna ya blackboard, pe lines ke aapsi rishte samjhaata hai: milne waali lines, samkon pe milne waali lines, aur kabhi na milne waali lines.

Intersecting lines aur unke chaar angles

Jab do lines samtal satah pe ek bindu pe milti hain, to ve intersect karti hain, aur do seedhi lines sirf ek hi bindu pe mil sakti hain. Ve chaar angles banaati hain, a, b, c aur d. Agar ∠a 120° hai, to ∠b 60° hai, kyunki dono milkar 180° ka seedha angle banaate hain. Isi tarah ∠c 120° aur ∠d 60° hai. ∠a aur ∠b jaise padosi angles linear pair hain, aur linear pair ka jod hamesha 180° hota hai. ∠b aur ∠d jaise aamne-saamne ke angles vertically opposite angles hain. Kyunki ∠a + ∠b = 180° aur ∠a + ∠d = 180°, isliye ∠b = ∠d hona chahiye, ∠a kuch bhi ho; isi tarah ∠a = ∠c. Aisa tark jo dikhaaye ki koi baat hamesha sach hai, proof kehlaata hai. Padho linear pair aur vertically opposite angles.

Naap aur geometry

Linear pair naapne pe 179° ya 181° aa sakta hai, ya do vertically opposite angles thode alag aa sakte hain. Protractor thoda galat rakha ja sakta hai, aur kheenchi gayi lines ki motaai hoti hai, jabki geometry ki aadarsh line ki koi motaai nahi hoti. Geometry aadarsh aakaaron ke saath kaam karti hai aur unke gun tark se nikaalti hai. Naap phir bhi tark ke anumaan ke bahut kareeb aate hain, isiliye geometry physics, kala, engineering aur architecture mein itni kaam aati hai.

Perpendicular lines

Agar kaatne ki jagah chaaron angles barabar hon, to har ek samkon, yaani 90°, hoga, kyunki chaaron milkar 360° hote hain. Samkon pe milne waali lines perpendicular kehlaati hain. Inka khada aur leta hona zaroori nahi: 90° pe milne waali koi bhi do lines perpendicular hain.

Parallel lines

Kuch line segments badhaane pe mil jaate lagte hain, aur kuch nahi. Railway ki patriyan, copy ki lines aur zebra crossing ki pattiyan kabhi milti nahi dikhtin. Parallel lines ek hi satah ki ve lines hain jo dono taraf kitna bhi badhaane pe nahi miltin. Dono shartein zaroori hain: table pe aur board pe kheenchi lines kabhi na milein, phir bhi ve alag satahon pe hain, isliye unhe parallel nahi kehte. Padho parallel aur perpendicular lines.

Kaagaz modna aur nishaan

Ek chaukor kaagaz lo. Uske aamne-saamne ke kinaare parallel hain aur padosi kinaare perpendicular. Use aadha leta modo: tah upar aur neeche ke kinaaron ke parallel teesri line hai. Har nayi tah pattiyan doguni karti hai, isliye n tahon ke baad 2ⁿ + 1 parallel lines milti hain: 3, 5, 9 waghera. Khadi tah in sabke perpendicular hoti hai. Chitron mein parallel lines ke ek set pe ek teer, doosre set pe do teer, aur samkon pe chhota square banaate hain.

Transversal aur corresponding angles

Do lines ko kaatne waali line transversal hai. Ye aath angles banaati hai, har kaatne ki jagah chaar, par har jagah vertically opposite angles ki do barabar jodiyan hoti hain, isliye zyaada se zyaada chaar alag naap. Dono kaatne ki jagahon pe ek hi sthaan ke angles, jaise ∠1 aur ∠5, corresponding angles hain. Lines parallel hon to corresponding angles barabar hote hain; aur agar ek corresponding jodi barabar ho, to lines parallel hain. Lines parallel na hon to corresponding angles kabhi barabar nahi ho sakte. Padho transversal ke angles.

Parallel lines banaana

Parallel lines banaane ke liye set square ko line l ke saath khisko aur uske kinaare se do lines kheencho. Dono l ke saath 90° banaati hain, isliye corresponding angles barabar hain aur lines 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 uska kinaara A tak na pahunche, aur line kheencho. Kaagaz modkar bhi: A se hokar l ke perpendicular tah t banao, phir A se hokar t ke perpendicular tah m: m, l ke parallel hai.

Alternate aur interior angles

Parallel lines waale chitra mein ∠d, ∠f ka alternate angle hai: dono lines ke beech, transversal ki ulti taraf. ∠f = ∠b kyunki ve corresponding angles hain, aur ∠b = ∠d kyunki ve vertically opposite hain, isliye ∠f = ∠d: alternate angles barabar hain. ∠3 aur ∠6 jaise angles, jo dono lines ke beech transversal ki ek hi taraf hain, interior angles hain, aur inka jod 180° hota hai. In baaton se ek angle pata ho to aathon nikal aate hain: agar ∠6 135° hai, to chaar angles 135° aur chaar 45° hain.

Parallel illusions

Kuch chitron mein parallel lines chhupi hoti hain: phaili lines ke upar ki lines mudi lagti hain, aur chhoti tirchhi lakeeron se kati lines jhuki lagti hain. Ruler dikhaata hai ki ve seedhi aur parallel hain; badalte angles pe kaatti peeche ki lines hamaari aankhon ko dhokha deti hain.

Aage badhne se pehle

Intersecting lines linear pair aur barabar vertically opposite angles banaati hain; perpendicular lines 90° pe milti hain; parallel lines kabhi nahi miltin; aur parallel lines pe transversal barabar corresponding aur alternate angles banaata hai, jabki interior angles ka jod 180° hota hai. Har sawaal, activity aur Figure it Out ke jawaab Chapter 5 ke NCERT solutions mein hain.