Kuch Bhujaayein aur Angles Diye Hon

Class 7 Maths · Chapter 7: Teen Kaat'ti Lines ki Kahaani · NCERT Ganita Prakash section 7.3

Seekho

Do bhujaayein aur beech ka angle: AB = 5 cm, AC = 4 cm, ∠A = 45° ke liye AB kheencho, A par protractor se 45° banao, us bhuja par A se 4 cm par C lagaao, aur BC jodo. Do angles aur beech ki bhuja: AB = 5 cm, ∠A = 45°, ∠B = 80° ke liye AB aur dono angles banao; bhujaayein C par kaat'ti hain.

Kya bhujaayein hamesha milti hain? Agar ∠A = 40°, to B ki bhuja ko aur tirchha karo. Jab dono bhujaayein parallel hon, interior angles milkar 180°, to ∠B = 140°. ∠B ≥ 140° par tribhuj nahi, AB ki lambaai kuch bhi ho. Niyam: tribhuj ke do angles ka jod 180° se kam.

∠A + ∠B < 180°

Angle jod gun: A se BC ke parallel line XY kheencho. To ∠XAB = ∠B aur ∠YAC = ∠C (alternate angles), aur ye ∠A ke saath seedha angle banaate hain. To har tribhuj ke liye ∠A + ∠B + ∠C = 180°. Ye chatur vichaar Yunaani ganitagya Euclid (lagbhag 300 BCE) ki mashhoor kitaab Elements mein milta hai.

∠A + ∠B + ∠C = 180°

To ∠B = 50° aur ∠C = 70° par ∠A = 180° − 120° = 60°. Agar ∠B = ∠C aur ∠A = 50°, to har ek (180° − 50°) ÷ 2 = 65°. Bahari angle: BC ko D tak badhaao. ∠ACD = 180° − ∠C = ∠A + ∠B: bahari angle saamne ke do andaruni angles ka jod.

∠ACD = ∠A + ∠B

Explore: chhoota angle.

1. Tribhuj mein ∠A = 50° aur ∠B = 60°. Angle ko ∠C tak kholo.
2. ∠A = 40°. Angle ko us sabse chhote ∠B tak kholo jahan bhujaayein parallel ho jaayein.

Yaad rakho

• Tribhuj do bhujaon aur beech ke angle se, ya do angles aur beech ki bhuja se ban sakta hai.
• Tribhuj ke angles milkar 180°; bahari angle saamne ke do andaruni angles ke jod ke barabar.

Quick check

Tribhuj ke do angles 75° aur 45°. Teesra?

1. 60°
2. 120°
3. 50°
4. 90°

Socho

Kya 180° ke beech wale angle aur do bhujaon se tribhuj banega?

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.