Class 7 Maths · Chapter 7
Short answer:
Class 7 Maths Chapter 7 "A Tale of Three Intersecting Lines" — Ganita Prakash ka chapter jisme intersecting lines, vertically opposite angles, linear pair, aur parallel lines ke saath transversal ke angle relationships (corresponding, alternate interior, co-interior) cover hote hain.
Chapter 7 "A Tale of Three Intersecting Lines" NCERT Class 7 Maths Ganita Prakash (2026-27 session) ka geometry-focused chapter hai jo intersecting lines aur parallel lines ke angle relationships ko ek exploratory andaaz mein cover karta hai. Ye chapter class 7 ke geometry foundation ke liye kaafi important hai kyunki isi ke concepts — vertically opposite angles, linear pair, aur transversal se bante corresponding/alternate/co-interior angles — aage ke higher classes ke coordinate geometry aur triangle properties (jaise iss hi book ke Geometric Twins chapter mein congruence) ke liye base banate hain.
Is page par hum NCERT Class 7 Maths Ganita Prakash chapter wise solutions ki series mein "A Tale of Three Intersecting Lines" ke sabhi in-text questions, exercise questions, formulas, aur common mistakes ko step-by-step, CBSE marking-scheme style mein cover kar rahe hain — taaki tumhe Ganita Prakash class 7 important questions ki achhi practice mil sake.
Chapter 7 Summary — 5 Minute Revision
Chapter 7 "A Tale of Three Intersecting Lines" ka core idea simple hai: jab do ya teen lines aapas mein intersect karti hain ya ek transversal parallel lines ko cut karti hai, to bante angles ke beech predictable relationships hote hain — vertically opposite angles equal, linear pair supplementary, aur parallel lines ke case mein corresponding/alternate angles equal jabki co-interior angles supplementary. In properties ko ache se practice karne se students Ganita Prakash class 7 important questions confidently solve kar sakte hain, aur ye base aage Geometric Twins jaise congruence-based chapters aur Constructions and Tilings jaisi practical geometry ke liye bhi kaam aata hai. Regular practice ke saath figure labeling par dhyan dena is chapter mein success ki key hai.
In-Text Questions — Solutions
Do lines ek point par intersect karti hain aur ek angle 90° hai. Baaki teen angles kya honge?
Jab ek angle 90° hota hai, to linear pair property se adjacent angle bhi 90° hoga.
∠1 = 90°, ∠2 = 180° − 90° = 90°
Vertically opposite angles equal hote hain, isliye ∠3 = ∠1 = 90° aur ∠4 = ∠2 = 90°.
Answer: Baaki teenon angles bhi 90° honge — matlab lines perpendicular hain.
Ek transversal do parallel lines ko cut karti hai. Agar corresponding angle 115° hai, to us line ka alternate interior angle kya hoga jo transversal ke opposite side par hai?
Pehle corresponding angle se uska vertically opposite angle nikalte hain, jo alternate interior angle ke barabar hota hai.
Corresponding angle = 115°
Vertically opposite angle = 115° (same value, opposite side)
Ye vertically opposite angle hi alternate interior angle ke position par match karta hai jab lines parallel hon.
Answer: Alternate interior angle = 115°.
Agar teen lines ek hi point se guzarti hain, to kitne angle pairs vertically opposite honge?
Teen concurrent lines total 6 angles banati hain jo ek point ke around hote hain.
6 angles ÷ 2 = 3 pairs
Har pair mein do angles ek doosre ke exactly opposite hote hain, jo equal hote hain.
Answer: 3 pairs of vertically opposite angles banenge.
Exercise Questions — Solutions (Q1–Q6)
Two lines l and m intersect at point O. If one angle formed is 35°, find all the other three angles.
Jab do lines ek point O par intersect karti hain, to 4 angles bante hain jo pairs mein linear pair (sum 180°) aur vertically opposite (equal) hote hain.
∠1 = 35° (diya hua)
∠2 = 180° − 35° = 145° (linear pair with ∠1)
∠3 = ∠1 = 35° (vertically opposite to ∠1)
∠4 = ∠2 = 145° (vertically opposite to ∠2)
Answer: Angles are 35°, 145°, 35°, 145°.
In the figure, line l is parallel to line m, and a transversal t cuts them. If one interior angle on one side is 70°, find the co-interior angle on the same side and the corresponding angle.
Co-interior angles (same-side interior angles) hamesha supplementary hote hain jab lines parallel hon.
Co-interior angle = 180° − 70° = 110°
Corresponding angles hamesha equal hote hain jab lines parallel hon (same position dono intersections par).
Corresponding angle = 70°
Answer: Co-interior angle = 110°, Corresponding angle = 70°.
Check whether the two lines in a figure are parallel if a transversal makes alternate interior angles of 62° and 62°.
Property: agar alternate interior angles equal hain, tab hi lines parallel hoti hain (converse of alternate angle theorem).
Given: alternate interior angles = 62° and 62°
Since 62° = 62°, alternate interior angles equal hain.
Answer: Haan, dono lines parallel hain.
Three lines are concurrent at a point, dividing the plane into 6 angles. If two adjacent angles among them are 40° and 50°, and the pattern of angles repeats symmetrically (vertically opposite triples), find all six angles.
Teen concurrent lines 6 angles banati hain jo vertically opposite pairs mein equal hote hain (3 pairs), aur ek complete round 360° hota hai.
Diye gaye do adjacent angles: 40° and 50°
Teesra adjacent angle (ek round mein 3 unique angles, har ek vertically opposite ke sath repeat) nikalne ke liye:
40° + 50° + x = 180° (kyunki teenon ek straight line ke ek side par hain)
x = 180° − 90° = 90°
Ab in teenon ka vertically opposite pair dusri taraf repeat hoga:
Answer: Six angles = 40°, 50°, 90°, 40°, 50°, 90° (total = 360°).
Draw two lines l and m that are perpendicular to the same line n. What can you conclude about l and m, and why?
Jab do lines kisi teesri line ke perpendicular hoti hain, to unke beech corresponding angles dono 90° hote hain — jo equal hain.
∠(l, n) = 90°, ∠(m, n) = 90°
Since corresponding angles equal hain (90° = 90°), converse of corresponding angles property ke anusar:
Answer: l aur m aapas mein parallel hain (l ∥ m), kyunki dono line n ke perpendicular hone se equal corresponding angles bana rahi hain.
A transversal cuts two lines such that the sum of interior angles on one side is 178°. Are the lines parallel? Justify.
Lines parallel hoti hain sirf tab jab co-interior (same-side interior) angles ka sum exactly 180° ho.
Given sum = 178° ≠ 180°
Since sum 180° se kam hai, dono lines ek side thodi si converge karengi (Euclid's parallel postulate ke anusar wo side milegi agar extend karein).
Answer: Nahi, lines parallel nahi hain — wo eventually intersect karengi us side jahan sum 180° se kam hai.
Important Equations — Ek Nazar Me
| Property | Rule |
|---|---|
| Linear pair | ∠1 + ∠2 = 180° (adjacent angles on a straight line) |
| Vertically opposite angles | ∠1 = ∠3 aur ∠2 = ∠4 (jab do lines intersect karti hain) |
| Sum of angles around a point | ∠1 + ∠2 + ∠3 + ∠4 + ... = 360° |
| Corresponding angles (parallel lines) | l ∥ m ⇒ corresponding angles equal |
| Alternate interior angles (parallel lines) | l ∥ m ⇒ alternate interior angles equal |
| Co-interior / same-side interior angles | l ∥ m ⇒ co-interior angles supplementary (sum = 180°) |
| Converse test for parallel lines | Agar corresponding ya alternate angles equal (ya co-interior sum 180°) ⇒ lines parallel hain |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Corresponding angles aur alternate interior angles ko confuse karna — dono equal hote hain lekin figure mein unki position alag hoti hai, isliye pehle diagram carefully label karo.
- Co-interior (same-side interior) angles ko galti se equal maan lena — ye actually supplementary hote hain (sum 180°), equal nahi.
- Linear pair aur vertically opposite angles mein farak bhool jaana — linear pair supplementary hote hain, vertically opposite equal hote hain.
- Ye assume kar lena ki koi bhi do lines automatically parallel hain bina angle-property check kiye — parallel prove karne ke liye corresponding/alternate angles equal ya co-interior sum 180° verify karna zaroori hai.
- Angles around a point ka total sum 360° hona bhool jaana jab multiple lines ek point par intersect karti hain — is wajah se calculation mein galat angle reh jaata hai.
- Figure mein transversal aur do lines ko sahi se identify na karna — kaunsi line transversal hai aur kaunsi do lines parallel hain, ye clear na hone se angle pairs galat ban jaate hain.
Board-Style Important Questions
- Class 7 Maths mein 'A Tale of Three Intersecting Lines' relatively naya chapter hai (rationalised Ganita Prakash syllabus 2023 ke baad se), isliye official CBSE board-style previous year papers is exact chapter naming ke saath abhi available nahi hain — school-level periodic tests mein iske concepts (vertically opposite angles, linear pair, parallel lines) practice ke liye pooche jaate hain.
- School unit tests mein aksar diagram-based questions aate hain jisme transversal ke angles find karke lines parallel hain ya nahi, ye justify karna hota hai.
- Vertically opposite aur linear pair angles par direct calculation questions common hote hain class tests mein.
- Practical drawing-based questions (ruler aur protractor use karke parallel lines aur transversal banana) bhi school assessments mein pooche jaate hain.
Aksar Poochhe Jaane Wale Sawaal
Class 7 Maths Chapter 7 'A Tale of Three Intersecting Lines' mein kya padhaya jaata hai?
Ye chapter Ganita Prakash (current NCERT, 2026-27 session) ka geometry chapter hai jisme intersecting lines, vertically opposite angles, linear pairs, aur transversal ke saath parallel lines ke angle relationships (corresponding, alternate interior, co-interior angles) cover hote hain. Practical drawing aur reasoning dono par focus hai.
Kya ye chapter purani NCERT ki 'Lines and Angles' chapter jaisa hi hai?
Concept overlap hai (angles, parallel lines ka basic idea), lekin naming aur framing rationalised Ganita Prakash book ke hisaab se badal gayi hai — is naye chapter ka focus teen lines ke ek saath intersect hone wale scenarios aur unke angle patterns explore karna hai, jo purani book ke isolated exercises se zyada exploratory hai.
Vertically opposite angles aur linear pair mein kya farak hai?
Vertically opposite angles wo hote hain jo do intersecting lines se bante hain aur ek doosre ke exactly opposite hote hain — ye hamesha equal hote hain. Linear pair adjacent angles hote hain jo ek straight line par milkar 180° banate hain — ye hamesha supplementary hote hain, equal nahi.
Transversal ke saath kitne types ke angle pairs important hain is chapter ke liye?
Teen main pairs important hain: corresponding angles (equal jab lines parallel hon), alternate interior angles (equal jab lines parallel hon), aur co-interior/same-side interior angles (supplementary, sum 180°, jab lines parallel hon). Inhi teenon ke converse se hum check karte hain ki lines parallel hain ya nahi.
Is chapter ke questions solve karne ka best approach kya hai?
Pehle figure ko carefully label karo (kaunsi line transversal hai, kaunse angles corresponding/alternate/co-interior hain), phir known angle property apply karo. Zyadatar mistakes angle-pair ko galat identify karne se hoti hain, isliye figure banakar angles ko clearly mark karna best strategy hai.
Kya calculator/protractor allowed hai practical geometry wale questions mein?
Class 7 ke is chapter mein zyadatar reasoning-based aur calculation-based questions hain jinhe bina protractor ke bhi angle properties (linear pair, vertically opposite, parallel line rules) se solve kiya ja sakta hai. Drawing-based activities mein protractor/ruler use karna diagram accuracy ke liye helpful hota hai, lekin final answer angle-property logic se hi aata hai.
Class 7 Maths — Saare Chapters
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