Teen Bhujaon se Tribhuj Banaana

Class 7 Maths · Chapter 7: Teen Kaat'ti Lines ki Kahaani · NCERT Ganita Prakash section 7.2

Seekho

4, 5 aur 6 cm bhujaon ka tribhuj: aadhaar AB = 4 cm kheencho. A se 5 cm ka aur B se 6 cm ka chaap kheencho. Ve C par kaat'te hain, aur △ABC mein AC = 5 cm, BC = 6 cm. Poore vritt nahi chahiye, bas kaatne jitne lambe chaap.

AB = 4 · AC = 5 · BC = 6

Har set nahi chalta. 3, 4 aur 8 cm aazmaao: chaap kabhi nahi milte. Kyun? Do binduon ke beech seedha raasta teesre bindu se hokar jaane se hamesha chhota hota hai. 10, 15, 30 wale tribhuj mein seedha raasta 30, 10 + 15 = 25 se lamba hoga: asambhav!

30 > 10 + 15 → no triangle

Triangle inequality: teen lambaaiyan tribhuj tabhi banaati hain jab har ek baaki do ke jod se kam ho. Shortcut: sirf sabse lambi jaancho. 4, 5, 8: 8 < 4 + 5 = 9, chalta hai. 2, 3, 6: 6 > 2 + 3, nahi chalta.

longest < sum of the other two

A aur B ke vritt socho (aadhaar = sabse lambi bhuja, radius = do chhoti). Radii ka jod AB se zyaada ho to vritt kaat'te hain: tribhuj. Theek barabar ho to bas chhoote hain: sapaat, tribhuj nahi. Kam ho to milte nahi. To 1 aur 100 bhujaon ke saath teesri 99 aur 101 ke beech honi chahiye.

1, 100: 99 < third < 101

Explore: tribhuj ya nahi?

1. Bhuja-lambaai ke set sort karo.

Yaad rakho

• Teen bhujaayein: aadhaar, phir siron se do chaap; kaat par teesra shirsh.
• Triangle inequality: sabse lambi bhuja baaki do ke jod se kam.

Quick check

Kaunse set se tribhuj ban sakta hai?

1. 5, 10, 12
2. 1, 1, 5
3. 3, 6, 9
4. 10, 20, 35

Socho

Tribhuj ki do bhujaayein 5 cm aur 5 cm. Teesri kya ho sakti hai?

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.