Transversal aur Corresponding Angles

Class 7 Maths · Chapter 5: Parallel aur Intersecting Lines · NCERT Ganita Prakash section 5.5–5.6

Seekho

Do lines l aur m ko kaatne wali line t transversal hai. Ye 8 angles banaati hai, yahan 1 se 8: l ke kaat par 1, 2, 3, 4 aur m ke kaat par 5, 6, 7, 8. Vertically opposite barabar hote hain (∠1 = ∠3, ∠2 = ∠4 …), to zyaada se zyaada 4 alag maap.

Dono kaaton par ek hi sthaan ke angles corresponding angles hain: ∠1 aur ∠5, ∠2 aur ∠6, ∠3 aur ∠7, ∠4 aur ∠8. Ishaan line l, 60° par transversal, aur t ke doosre bindu se 60° banaati line m kheenchta hai. l aur m parallel nikalti hain!

Dono taraf se: corresponding angles barabar to lines parallel. Aur lines parallel to corresponding angles barabar (ek ko tracing paper par utaaro: doosre par theek baithta hai). Agar l aur m parallel nahi, to corresponding angles kabhi barabar nahi.

∠2 = ∠6 ⇔ l ∥ m

To parallel lines mein sirf do maap bachte hain. Agar ∠2 = 65°: ∠4, ∠6, ∠8 bhi 65°, aur ∠1, ∠3, ∠5, ∠7 = 180° − 65° = 115°. Corresponding angles parallel ki jaanch dete hain, lines ko hamesha tak badhaaye bina.

Explore: line m ghumao.

1. Line m ko l ke parallel hone tak ghumao.
2. Ab ∠6 = 75° banao. Kya lines parallel hain?

Yaad rakho

• Transversal 8 angles banaati hai; corresponding angles har kaat par ek hi sthaan par.
• Corresponding angles theek tab barabar jab lines parallel.

Quick check

l ∥ m aur ∠3 = 110°. ∠7 kitna?

1. 110°
2. 70°
3. 180°
4. 55°

Socho

Kya transversal ke 8 mein se 5 angles ke maap sab alag ho sakte 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.