Class 7 Maths Ch 5 NCERT Solutions Hinglish mein

Ganita Prakash, Class 7 Maths textbook Part 1 (Reprint 2026-27) ke Chapter 5, Parallel and Intersecting Lines, ke har sawaal ke jawaab: text ke sawaal, Activity 1 se 6, hal kiye udaaharan aur teenon Figure it Out sets. Page numbers kitaab ke hisaab se hain (pages 107–126). Kheenchne waale kaamon ke jawaab batate hain ki kya kheenchna hai aur kaise jaanchna hai. Chhote notes: Chapter 5 ke notes.

Across the Line (pages 107–108)

Mude kaagaz ki lines. Kuch jodiyan kaagaz pe hi milti hain. Jo nahi miltin, unmein se kuch ek taraf paas aati hain aur kaagaz ke baahar badhaane pe mil jaayengi; kuch ek hi doori pe rehti hain aur kabhi nahi milengi.

Do intersecting lines kitne angles banaati hain? Chaar.

Kya do seedhi lines ek se zyaada bindu pe kaat sakti hain? Nahi. Do seedhi lines sirf ek bindu pe mil sakti hain; kaatne ke baad ve aur door hoti jaati hain.

Activity 1: chaar angles ka pattern. Aamne-saamne ke angles barabar hain, ∠a = ∠c aur ∠b = ∠d, aur padosi angles ka jod 180° hai, jaise ∠a + ∠b = 180° aur ∠b + ∠c = 180°.

Agar ∠a 120° hai, to ∠b, ∠c aur ∠d nikaalo. ∠a aur ∠b seedha angle banaate hain, isliye ∠b = 180° − 120° = 60°. Phir ∠c = 180° − 60° = 120° aur ∠d = 180° − 120° = 60°.

Kya ye har jodi intersecting lines ke liye sach hai? Haan. Seedha angle 180° ka hai, isliye ∠a + ∠b = 180° aur ∠a + ∠d = 180°, yaani ∠a kuch bhi ho, ∠b = ∠d. Isi tarah ∠b + ∠a = ∠b + ∠c = 180°, isliye ∠a = ∠c. Vertically opposite angles hamesha barabar hain.

Lines l aur m kaatti hain: ∠a = 120°, ∠b = 60°, ∠c = 120°, ∠d = 60°, aur vertically opposite angles barabar hone ka tark — Do lines kaatti hain: chaar angles

Figure it Out (page 108)

Fig. 5.3. Linear pairs: ∠a aur ∠b, ∠b aur ∠c, ∠c aur ∠d, ∠d aur ∠a. Vertically opposite jodiyan: ∠b aur ∠d, aur ∠a aur ∠c.

Naapne pe linear pair 180° kyun nahi aata? Naapne ki galtiyon ki wajah se, jaise protractor theek se na rakhna, aur isliye ki kheenchi lines moti hoti hain jabki geometry ki aadarsh line ki koi motaai nahi. Sahi maan tark batata hai; naap sirf kareeb aate hain.

Perpendicular Lines (pages 108–109)

Kya chaaron angles barabar waali kaatti lines kheench sakte ho? Haan: chaaron ka jod 360° hai, isliye har ek 90° hoga. Aisi lines perpendicular hain.

Perpendicular lines ki do jodiyan, ek leti-khadi aur ek tirchhi ghumaai hui, dono pe chhota square — Perpendicular lines

Between Lines (page 109)

Fig. 5.5 ka varnan. Sample varnan (angles protractor se naapo):

FG aur FH apne saajhe endpoint F pe milte hain aur 115.3° ka angle banaate hain.
AB aur CD bindu X pe kaatte hain, jo CD ke beech ke kareeb hai; X pe chaaron angles vertically opposite ki do barabar jodiyan banaate hain, aur padosi angles ka jod 180° hai.
IJ aur LM bindu Y pe kaatte hain, dono segments ke beech ke kareeb; yahan bhi aamne-saamne ke angles barabar hain aur padosi angles ka jod 180° hai.
ST aur UV nahi milte, aur OP aur QR bhi nahi.

Kya ST aur UV badhaane pe milenge? Ye T aur V ki taraf thoda paas aate hain, isliye us taraf kaafi badhaane pe shaayad mil jaayenge.

Kya OP aur QR badhaane pe milenge? Ye lagbhag ek hi doori pe rehte hain, isliye milne ki sambhaavna nahi: ye parallel lagte hain.

Parallel lines (page 110)

Classroom mein parallel lines: blackboard, darwaaze ya desk ke aamne-saamne ke kinaare; copy ki lines; tiles ki kataarein; khidki ki salaakhein.

Fig. 5.6: kaunsi lines parallel lagti hain? a, h aur i; c aur g; f aur d; aur b aur e.

Figure 5.6 disha ke hisaab se rangon mein: a, h, i khadi; c, g leti; d, f neeche jhukti; b, e upar jaati — Kaunsi lines parallel hain? (Fig. 5.6)

Activity 2: chaukor kaagaz modna (page 111)

Aamne-saamne ke kinaare: parallel.
Padosi kinaare: perpendicular.
Ek leti tah ke baad 3 parallel lines: do kinaare aur tah. Nayi tah khade kinaaron ke perpendicular hai.
Ek aur tah ke baad 5 parallel lines; phir ek aur pe 9. Pattern: har tah pattiyan doguni karti hai, isliye n tahein 2ⁿ + 1 parallel lines deti hain, aur agli tah 17 degi. (Extra: NCERT ki answer key ise “2n + 1” likhti hai, jo 3 tahon pe 9 nahi deta; matlab 2ⁿ + 1 hai.)
Khadi tah leti lines ke perpendicular hai.
Haan: diagonal se bahar ka ek kona aise modo ki uski nok chaukor ke beech, diagonal ki tah pe, chhue; nayi tah diagonal ke parallel hogi.

Chaukor kaagaz bina tah, phir 1, 2 aur 3 tahon ke saath, 2, 3, 5 aur 9 parallel lines, aur unke perpendicular khadi tah — Aadha modo, baar-baar

Ek aur modne waali activity (page 112)

Kya a, b aur c kramashah p, q aur r ke parallel hain? Haan. a aur p upar aur neeche ke kinaaron pe hain, jo parallel hain. b aur q khadi tahon pe hain, dono un kinaaron ke perpendicular, isliye parallel hain. c aur r do aamne-saamne ke kone kaatne waali tahein hain, dono chaukor ke ek hi diagonal ke parallel, isliye parallel hain.

Figure it Out (pages 113–114)

1. Dot paper pe perpendicular. Leti segment ke liye khadi line kheencho; khadi ke liye leti. 1 aage, 1 upar jaane waale segment ke liye 1 aage, 1 neeche jaane waali line. 2 aage, 3 neeche jaane waale segment ke liye 3 aage, 2 upar jaane waali line. Niyam: dono kadam ki ginti badlo aur ek ki disha ulat do.

Dot paper pe chaar segments, har ek ke saath laal perpendicular aur samkon ka nishaan — Figure it Out 1

2. Fig. 5.11 pe nishaan. Ek hi disha ki bhujaaon pe ek jaise teer, aur jahan leti bhuja khadi bhuja se milti hai wahan square.
(a) Perpendicular bhujaayein wahan pehchaani jahan ek bhuja leti grid line pe aur doosri khadi grid line pe ho.
(b) Parallel bhujaayein ek hi disha waali bhujaayein hain: dono leti, dono khadi, ya ek jaise kadam waali tirchhi bhujaayein, jaise 1 khaana aage pe 1 khaana upar.

Figure 5.11 ki aakritiyan, parallel bhujaaon pe ek jaise teer aur perpendicular bhujaaon pe chhote square ke saath — Figure it Out 2

3. Dot paper pe parallel lines ke sets. Alag dots se ek jaise kadam waale segments kheencho, jaise kai leti, kai khadi, aur kai 1 aage, 2 upar jaane waale.

4. Fig. 5.12 ke segments ke parallel.
(a) Haan, kuch doosron se mushkil the.
(b) 45° se alag tirchhe: e, f, g aur h.
(c) Segment ke dot kadam gino aur kisi doosre dot se wahi kadam dohraao: e 1 daayein aur 3 neeche, f 1 daayein aur 6 neeche, g 5 daayein aur 2 upar, aur h 10 daayein aur 3 neeche.

Figure 5.12 ke segments, e, f, g aur h ke parallel rangon mein, aur har segment ke dot kadam — Figure it Out 4

5. Fig. 5.13: b ya c, kaunsa a ke parallel hai? Line c. Yahan aankh dhokha kha sakti hai, isliye transversal use karo: upar ke bindu ko a ke neeche ke sire se jodne waali line a aur c ke saath barabar alternate angles banaati hai, isliye a aur c parallel hain. Line b, a se door mudti hai.

Lines a, b aur c, jodne waali line transversal ke roop mein: barabar alternate angles dikhaate hain ki c, a ke parallel hai — Figure it Out 5

Transversals (page 115)

Kya aathon angles alag ho sakte hain? Nahi. Har kaatne ki jagah vertically opposite angles barabar hain: ∠1 = ∠3, ∠2 = ∠4, ∠5 = ∠7 aur ∠6 = ∠8. Isliye zyaada se zyaada chaar alag naap.

Kya ∠6, ∠5, ∠4, ∠3 aur ∠2 paanchon alag ho sakte hain? Nahi, kyunki ∠2 = ∠4, isliye in paanch mein se zyaada se zyaada chaar alag ho sakte hain.

Transversal t lines l aur m ko kaatti hai, aath angles ki numbering aur barabar vertically opposite jodiyan ek jaise rang mein — Transversal: aath angles

Activity 3, 4 aur 5 (pages 115–117)

Activity 3. Kadam follow karne pe X pe ∠a = 60° aur Y pe ∠b = 60°; sirf do alag naap dikhte hain, 60° aur 120°. l aur m ke baare mein kya dikhta hai? Ve parallel hain. Barabar corresponding angles ka matlab parallel lines.

Activity 4. Fig. 5.19 ki parallel lines pe ek jaise teer ke nishaan hain. Tracing paper pe utaara ∠a, ∠b pe bilkul baith jaata hai, aur har corresponding jodi ka naap ek jaisa aata hai: parallel lines ko kaatne waale transversal ke corresponding angles barabar hain.

Activity 5. Haan, mushkil hai; asal mein ye ho hi nahi sakta. Fig. 5.20 ki lines l aur m parallel nahi hain, aur jab do lines parallel na hon, to koi transversal unki corresponding jodi barabar nahi bana sakta.

Parallel lines l aur m ko transversal t kaatta hai, corresponding jodiyon 1 aur 5, 2 aur 6, 3 aur 7, 4 aur 8 ke saath — Corresponding angles

Drawing Parallel Lines (pages 118–119)

Kya set square se kheenchi do lines parallel hain? Haan. Dono l ke saath 90° banaati hain; l ko transversal maano to corresponding angles dono 90° hain, isliye lines parallel hain.

Set square ki lambi bhuja se kheenchi lines (Fig. 5.22). Ye bhi parallel hain: dono l ke saath ek jaisa angle banaati hain, isliye corresponding angles barabar hain. Ek angle ko doosre pe trace karke, ya dono ko protractor se naapkar jaancho.

Figure it Out: A se l ke parallel line. Auzaar: ruler, set square aur pencil. Set square ka ek kinaara l pe rakho, doosre kinaare se ruler kaskar sataao, set square ko ruler ke saath tab tak khisko jab tak pehla kinaara A se na guzre, aur us kinaare se line kheencho. Nayi line l ke parallel hai.

Set square se parallel lines: l pe do perpendicular, aur ruler ke saath khiskaakar bindu A se parallel — Set square se parallel lines

Kaagaz modne mein (Fig. 5.24) l aur m parallel kyun hain? Tah t, l ke perpendicular hai, aur m, t ke perpendicular. t ko transversal maano to l aur m pe corresponding angles dono 90° hain, isliye l aur m parallel hain.

Modkar A se parallel: tah l, A se l ke perpendicular tah t, phir A se t ke perpendicular tah m — Modkar A se parallel

Alternate Angles aur udaaharan (pages 120–122)

Activity 6: agar ∠f 120° hai, to ∠d kitna? 120°. ∠b, ∠f ka corresponding hai, isliye ∠b = 120°, aur ∠d, ∠b ka vertically opposite hai, isliye ∠d = 120°. Ye ∠f ke kisi bhi naap pe chalta hai, isliye lines parallel hon to alternate angles hamesha barabar hain.

Alternate angles: f aur b corresponding hone se barabar, aur b aur d vertically opposite hone se barabar, isliye f = d — Alternate angles barabar hain

Example 1 (∠6 = 135°): ∠2, ∠4, ∠6 aur ∠8 135° hain; ∠1, ∠3, ∠5 aur ∠7 45° hain. Example 2 (∠a = 120°, ∠f = 70°): ∠b = 60°, jo apne corresponding ∠f ke barabar nahi, isliye l aur m parallel nahi hain. Example 3 (∠3 = 50°): ∠6 = 130°. Example 4: ∠CAB = 55°, ∠ABC = 60° aur ∠BCD = 120°.

Kya ∠3 aur ∠6 mein koi rishta hai? Haan: inka jod hamesha 180° hota hai. Proof: linear pair hone se ∠2 + ∠3 = 180°, aur corresponding hone se ∠2 = ∠6, isliye ∠3 + ∠6 = 180°. Parallel lines ko kaatne waale transversal ki ek taraf ke interior angles ka jod 180° hota hai.

Parallel lines ko transversal kaatta hai: ∠3 = 50° aur ∠6 = 130°, ∠4 = 130° aur ∠5 = 50°, interior angles ka jod 180° — Interior angles ka jod 180°

Figure it Out (pages 123–125)

1. Fig. 5.30 ke angles. a = 48°, b = 52°, c = 81°, d = 99°, e = 69°, f = 48°, g = 122°, h = 75°, i = 54°, j = 97°. Kaaran diagram mein hain.

Figure it Out 1 ke jawaab, a se j tak har angle ke kaaran ke saath — Figure it Out 1: jawaab

2. Fig. 5.31 mein angle a.
(i) a = 180° − 42° = 138°; 100° ki zaroorat nahi.
(ii) a = 180° − 62° = 118°.
(iii) Tirchhi line parallel lines ke saath 180° − 110° = 70° banaati hai, aur agli line 35° aur mudti hai, isliye a = 70° + 35° = 105°.
(iv) Khadi line base ke perpendicular hai, isliye tirchhi lines ke saath 90° − 67° = 23° banaati hai, aur alternate angles se a = 23°.

Figure it Out 2 ki chaaron aakritiyan dobaara, a = 138°, 118°, 105° aur 23° ke saath — Figure it Out 2: jawaab

3. Fig. 5.32 mein x aur y.
(i) Khadi line parallel lines ke perpendicular hai, aur tirchhi line uske saath 65° banaati hai, isliye tirchhi line parallel lines ke saath 90° − 65° = 25° banaati hai. x = 25° aur y = 180° − 25° = 155°.
(ii) Dono lines neeche ki parallel ke saath 53° aur 78° banaati hain, isliye upar ki parallel ke saath bhi, jahan ve milti hain; x = 78° − 53° = 25°.

Figure it Out 3 ki dono aakritiyan dobaara, x = 25°, y = 155°, aur x = 25° ke saath — Figure it Out 3: jawaab

4. Fig. 5.33. ∠GEH = 45°: corresponding hone se ∠DEB = ∠ABC, aur ∠GEH, ∠DEB ka vertically opposite hai. ∠FED = 78°: corresponding hone se ∠GEK = ∠IKJ, aur ∠FED, ∠GEK ka vertically opposite hai. ∠HEF = 180° − 45° − 78° = 57°, kyunki teenon angles GD pe seedha angle banaate hain.

Figure it Out 4 dobaara, E pe ∠GEH = 45°, ∠HEF = 57° aur ∠FED = 78° — Figure it Out 4: jawaab

5. Fig. 5.34. ∠BEF = 55° tirchhi line BE aur khadi EF ke beech ka angle hai. AB, CD aur EF parallel hain, isliye B aur D pe tirchhi line upar ki khadi disha ke saath 55° banaati hai (alternate angles), aur uske neeche ke angles x aur y 180° − 55° = 125° hain. To x = y = 125°.

Figure it Out 5 dobaara, x = y = 125° ke saath — Figure it Out 5: jawaab

6. Fig. 5.35 mein ∠NOP. N aur O se LM aur PQ ke parallel lines kheencho. N pe 96° do hisson mein bantta hai: 40°, jo M ke 40° ka alternate hai, aur 96° − 40° = 56°. O pe ON ke saath 56° (N ke 56° ka alternate) aur OP ke saath 52° (P ke 52° ka alternate). Isliye ∠NOP = 56° + 52° = 108°.

Figure it Out 6, N aur O se LM ke parallel lines ke saath: 96° = 40° + 56° aur ∠NOP = 56° + 52° = 108° — Figure it Out 6: jawaab

Parallel Illusions (page 125)

Ye illusions kyun hote hain? Parallel lines ko peeche ki lines lagaataar badalte angles pe kaatti hain, ek chitra mein phaili lines aur doosre mein chhoti tirchhi lakeerein. Aise kaatne ke paas hamaari aankhein line ki disha galat aankti hain, isliye seedhi parallel lines mudi ya jhuki lagti hain. Ruler dikhaata hai ki ve seedhi aur parallel hain. (Extra: inhe Hering aur Zöllner illusions kehte hain.)

Do illusions: phaili lines ke upar laal parallel lines mudi lagti hain, aur tirchhi lakeeron waali parallel lines jhuki lagti hain — Parallel illusions

Chhote notes aur practice topic pages pe hain: linear pair aur vertically opposite angles, parallel aur perpendicular lines aur transversal ke angles.

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