Class 7 Maths · Chapter 5
Short answer:
Chapter 5 "Parallel and Intersecting Lines" Class 7 Ganita Prakash geometry ka foundation chapter hai — ismein intersecting lines ke vertically opposite angles aur linear pair, aur transversal se banne wale corresponding, alternate, aur co-interior angles cover hote hain, saath hi ruler-set square se parallel lines construct karna bhi sikhaya jaata hai.
Class 7 Maths Ganita Prakash ka Chapter 5, "Parallel and Intersecting Lines", geometry ki bunyaad majboot karta hai — yeh chapter sikhata hai ki lines ek doosre ke saath kaise interact karti hain: kabhi cross karke angles banati hain, aur kabhi hamesha ke liye ek doosre se equal distance par chalti rehti hain, kabhi mil hi nahi paatin.
Is chapter me intersecting lines se bane vertically opposite angles aur linear pairs, phir transversal ke through parallel lines ke corresponding, alternate, aur co-interior angles — sab kuch practical construction (ruler-set square) ke saath explain kiya gaya hai. Yeh chapter aage chalke "A Tale of Three Intersecting Lines" aur "Constructions and Tilings" jaise chapters ki base banata hai, isliye concepts clear hona zaroori hai.
Chapter 5 Summary — 5 Minute Revision
Chapter 5, "Parallel and Intersecting Lines", Class 7 Ganita Prakash ke geometry section ki neev hai. Do lines ek plane me ya toh intersect karti hain, ya parallel hoti hain, ya coincide karti hain — aur inke beech ke angle-relationships hi is chapter ka core hain.
Jab do lines intersect karti hain, 4 angles bante hain jinme vertically opposite angles equal hote hain aur linear pair angles ka sum 180° hota hai. Jab ek transversal do parallel lines ko cut karta hai, toh 8 angles bante hain — corresponding, alternate interior, aur alternate exterior angle pairs equal hote hain, jabki co-interior angle pairs ka sum 180° hota hai.
Yeh chapter practical construction skills bhi build karta hai — ruler aur set square se accurately parallel lines draw karna, jo aage Constructions and Tilings chapter me deeper practical geometry ke liye zaroori hai. In concepts ki pakad A Tale of Three Intersecting Lines chapter ko samajhne ke liye bhi essential hai, jahan multiple lines aur triangles ke angle-relationships explore hote hain. Overall, yeh chapter reasoning-based geometry ki shuruaat hai jo higher classes tak carry hoti hai.
In-Text Questions — Solutions
Figure it Out (Page start): Do lines ek plane me kis-kis tarah se position ho sakti hain?
Do lines ek plane me teen tarike se ho sakti hain:
1. Intersecting lines — jo ek point par cross karti hain.
2. Parallel lines — jo kabhi meet nahi karti, unke beech distance constant rehta hai.
3. Coincident lines — jo poori tarah overlap kar jaati hain (ek hi line ban jaati hain).
Jab do lines intersect karti hain toh kitne angles banate hain aur unme kya relation hota hai?
Jab do lines ek point par intersect karti hain, total 4 angles bante hain.
Opposite pairs equal hote hain (vertically opposite angles)
Adjacent pairs ka sum 180° hota hai (linear pair)
Example: agar ek angle 50° hai, toh uske adjacent angles 130°, 50° aur 130° honge.
Kya set square se hum kisi bhi line ke parallel line draw kar sakte hain? Method batao.
Haan, set square aur ruler ka combination use karke koi bhi parallel line draw kar sakte hain:
1. Ruler ko diye gaye line ke saath fix karo.
2. Set square ka ek edge ruler ke saath slide karo, dusra edge line ko touch kare.
3. Set square ko ruler ke saath slide karke desired position par le jao.
4. Us position par line khींच do — yeh original line ke parallel hogi.
Transversal se bane angles me se konse pairs 'equal' hote hain aur konse 'supplementary' (180°)?
Equal angle pairs: Corresponding angles, Alternate interior angles, Alternate exterior angles, aur Vertically opposite angles.
Supplementary pairs (180°): Co-interior (same-side interior) angles, aur Linear pair angles.
Yeh property tabhi apply hoti hai jab do lines parallel hon aur ek transversal unhe cut kare.
Exercise Questions — Solutions (Q1–Q5)
1. Draw a line l and a point A not on it. Draw a line m through A parallel to l. How many such lines can be drawn?
Solution: Point A ek fixed point hai jo line l par nahi hai.
Set square/ruler method se: A se hoke line l ke parallel sirf ek hi line khinchi ja sakti hai.
Yeh Playfair's Axiom (parallel postulate ka modern form) confirm karta hai — "given a line and a point not on it, exactly one line parallel to the given line passes through that point."
Answer: Sirf 1 line.
2. Two lines p and q intersect at point O such that ∠POQ = 65°. Find all the other three angles.
Solution: Jab do lines ek point O par intersect karti hain, 4 angles bante hain jo pairs me linear pair aur vertically opposite hote hain.
Diya hai: ∠POQ = 65°
Vertically opposite angle: ∠ROS = ∠POQ = 65° (vertically opposite angles equal hote hain)
Linear pair se: ∠POQ + ∠QOR = 180° (linear pair, straight line par)
∠QOR = 180° − 65° = 115°
Vertically opposite: ∠SOP = ∠QOR = 115°
Answer: Angles hain — 65°, 115°, 65°, 115°
3. In the figure, line AB || line CD and a transversal PQ cuts them. If one interior angle is 110°, find all the other seven angles.
Solution: Jab transversal do parallel lines ko cut karta hai, 8 angles bante hain — inme se corresponding angles equal, alternate angles equal, aur co-interior angles supplementary hote hain.
Diya hai: ek interior angle = 110°
Uska linear pair angle = 180° − 110° = 70°
AB line par: do angles 110° aur 70° (linear pair — alternate wale)
Corresponding angle property se, CD line par bhi same pattern repeat hota hai:
Angles = 110°, 70°, 110°, 70° (line AB par) aur 110°, 70°, 110°, 70° (line CD par)
Answer: Total 8 angles me se 4 angles 110° ke aur 4 angles 70° ke honge — alternate wale equal, co-interior wale 180° tak add honge.
4. Using a ruler and set square, draw a line parallel to a given line l at a distance of 4 cm from it.
Solution (steps):
1. Line l khींचो aur usme do points A aur B lo.
2. A aur B par line l ke perpendicular khींचो (set square use karke).
3. Dono perpendiculars par A aur B se 4 cm ki duri par points A' aur B' mark karo.
4. A' aur B' ko milao — yehi required line m hai jo l ke parallel hai aur 4 cm distance par hai.
Verification: Do lines jo ek hi third line (transversal/perpendicular) se equal distance par honi aur equal angles (90°) banati hain, wo parallel hoti hain — isi property se construction sahi sabit hota hai.
5. In a figure, three lines meet at a point such that one pair of vertically opposite angles is (2x + 20)° and (3x − 10)°. Find x and all six angles formed.
Solution: Vertically opposite angles hamesha equal hote hain, isliye:
2x + 20 = 3x − 10
20 + 10 = 3x − 2x
x = 30
Angle value = 2(30) + 20 = 80°
Teen lines ek point se guzarti hain to 6 angles bante hain, jinka sum 360° hota hai (ek full round), aur ye 3 pairs of vertically opposite angles me bantay hain.
Ek pair (80°, 80°) hai. Baaki 2 pairs (4 angles) ka combined sum:
360° − 2(80°) = 200°, matlab baaki do pairs mila kar 100° + 100° honge — par exact split figure ke exact configuration (baaki angles ke beech ke actual measure) par depend karega, jo is question me nahi diya gaya.
Answer: x = 30, ek pair of vertically opposite angles = 80° each; baaki angles figure ki extra jaankari ke bina uniquely determine nahi ho sakte.
Important Equations — Ek Nazar Me
| Concept | Rule / Property |
|---|---|
| Linear Pair | Do adjacent angles jo ek straight line banate hain, unka sum = 180° |
| Vertically Opposite Angles | Do lines ke intersection se bane opposite angles hamesha equal hote hain |
| Angles around a point | Ek point ke around bane sabhi angles ka sum = 360° |
| Corresponding Angles (parallel lines + transversal) | Same side, same position ke angles equal hote hain |
| Alternate Interior Angles | Transversal ke opposite side ke interior angles equal hote hain |
| Alternate Exterior Angles | Transversal ke opposite side ke exterior angles equal hote hain |
| Co-interior (Allied) Angles | Same side ke interior angles ka sum = 180° |
| Playfair's Axiom | Ek point se (jo line par nahi hai) us line ke parallel sirf ek hi line khinchi ja sakti hai |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Vertically opposite angles ko linear pair samajh lena — student angle ko 180° − angle bana dete hain jabki vertically opposite angles equal hote hain, subtract nahi karte.
- Corresponding angles aur alternate angles ke position confuse kar dena — dono equal hote hain lekin unki figure me position (same-side vs opposite-side) galat identify ho jaati hai.
- Co-interior angles ko bhi 'equal' maan lena, jabki inka sum 180° hota hai — yeh galti bahut common hai kyunki baaki sab pairs equal hote hain.
- Parallel lines draw karte waqt set square ko sahi se align na karna, jisse constructed line thodi si tilt ho jaati hai aur exactly parallel nahi banti.
- Angles measure karte waqt protractor ka zero line galat point se align karna, jisse angle value 5-10° tak galat aa jaati hai.
- Figure me diya hua ek angle dekh kar bina transversal aur parallel lines ka relationship samjhe seedha answer likh dena — properties apply karne se pehle figure carefully analyze na karna.
Board-Style Important Questions
- Class 7 periodic/unit tests me is chapter se transversal diagrams diye jaate hain jisme ek angle value se baaki saat angles nikalne ko kaha jaata hai.
- Ruler-compass/set square se ek diye gaye point se parallel line construct karne ka practical-based question aata hai.
- Vertically opposite angles aur linear pair identify karke unki values find karne wale short-answer questions common hain.
- 'True/False' ya 'Fill in the blanks' type questions is chapter ki basic definitions (parallel, intersecting, coincident lines) par based hote hain.
- Real-life examples (jaise railway tracks, ruled notebook lines, zebra crossing) se parallel/intersecting lines identify karwane wale conceptual questions puchhe jaate hain.
Aksar Poochhe Jaane Wale Sawaal
Class 7 Maths Chapter 5 'Parallel and Intersecting Lines' me kya-kya topics cover hote hain?
Is chapter me intersecting lines, parallel lines, transversal, corresponding angles, alternate angles, co-interior (allied) angles, vertically opposite angles, linear pair, aur ruler-compass/set-square se parallel lines ki construction cover hoti hai. Yeh Ganita Prakash book ka geometry-focused chapter hai jo practical drawing aur reasoning dono par based hai.
Parallel lines aur intersecting lines me kya farak hai?
Parallel lines wo lines hoti hain jo same plane me hone ke baad bhi kabhi meet nahi karti — unke beech ki perpendicular distance hamesha constant rehti hai. Intersecting lines wo hoti hain jo ek common point par cross karti hain aur wahan angles bante hain (jinme vertically opposite aur linear pair shamil hain).
Transversal kya hota hai aur uske angles kaise pehchane jaate hain?
Jab ek line do ya zyada lines ko do alag points par cut karti hai, use transversal kehte hain. Transversal se 8 angles bante hain — inme corresponding angles (same position), alternate interior/exterior angles (opposite sides, equal), aur co-interior angles (same side, sum 180°) important hote hain.
Kaise pata karein ki do lines parallel hain ya nahi (transversal use karke)?
Agar corresponding angles equal hain, ya alternate angles equal hain, ya co-interior angles ka sum 180° hai — toh dono lines parallel hain. Yeh converse property construction aur proof dono me use hoti hai.
Ganita Prakash Class 7 ke baaki chapters kahan se solutions milenge (jaise Large Numbers Around Us, Arithmetic Expressions)?
Poore NCERT Class 7 Maths Ganita Prakash chapter wise solutions — jaise Large Numbers Around Us, Arithmetic Expressions, A Peek Beyond the Point, Expressions Using Letter-Numbers, Number Play, A Tale of Three Intersecting Lines, Working with Fractions, Geometric Twins, Operations with Integers, Finding Common Ground, Connecting the Dots, Constructions and Tilings, Finding the Unknown — hamari site par step-by-step available hain, is chapter jaisi hi detailed working ke saath.
Kya purane NCERT ke Data Handling, Symmetry, Exponents and Powers jaise chapters is naye Ganita Prakash book me hain?
Nahi — 2026-27 session ki rationalised Ganita Prakash book me Data Handling, Comparing Quantities, Perimeter and Area, Exponents and Powers, Symmetry, Visualising Solid Shapes, aur The Triangle and its Properties standalone chapters ki tarah nahi hain. Inme se kuch concepts (jaise congruence-related triangle work) ab dusre chapters jaise Geometric Twins me integrate ho gaye hain.
Class 7 Maths — Saare Chapters
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