Line ke Aar-Paar aur Perpendicular Lines

Class 7 Maths · Chapter 5: Parallel aur Intersecting Lines · NCERT Ganita Prakash section 5.1–5.2

Seekho

Zoya kaagaz ka varg kuch baar modti hai aur silvaton par lines kheenchti hai. Kuch lines ek bindu par milti hain: hum kehte hain ve intersect karti hain. Do seedhi lines sirf ek bindu par mil sakti hain. Jahan do lines kaat'ti hain, chaar angles bante hain, yahan a, b, c aur d.

Agar ∠a = 120°, to ∠a aur ∠b milkar seedha angle banaate hain, to ∠b = 180° − 120° = 60°. Waise hi ∠c = 120° aur ∠d = 60°. a aur b jaise agal-bagal ke angles linear pair hain: linear pair hamesha milkar 180°.

∠a + ∠b = 180°

Ye hamesha sach kyun? ∠a + ∠b = 180° aur ∠a + ∠d = 180°, to ∠b aur ∠d barabar hone hi chahiye, ∠a kuch bhi ho. b aur d jaise aamne-saamne ke angles vertically opposite angles hain, aur hamesha barabar. Har baar sach dikhaane wala tark proof kehlaata hai.

∠b = ∠d · ∠a = ∠c

Naapne par linear pair 179° ya 181° aa sakta hai: banaayi lines mein motaai hoti hai aur protractor padhne mein chhoti galtiyan. Geometry aadarsh lines se tark karti hai. Agar chaaron angles barabar hon, to har ek 360° ÷ 4 = 90°, aur lines perpendicular hain.

4 equal angles → 90° each

Explore: linear pair ya vertically opposite?

1. Do kaat'ti lines ke angle-jodon ko sort karo.

Yaad rakho

• Do kaat'ti lines 4 angles banaati hain: linear pair milkar 180°, vertically opposite barabar.
• 90° par kaat'ti lines perpendicular hain.

Quick check

Do lines kaat'ti hain aur ek angle 35° hai. Chaaron angles kaunsi list ho sakti hai?

1. 35°, 145°, 35°, 145°
2. 35°, 35°, 35°, 35°
3. 35°, 55°, 35°, 55°
4. 35°, 145°, 145°, 35°

Socho

Kya do seedhi lines do alag binduon par mil sakti hain?

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.