Alternate Angles

Class 7 Maths · Chapter 5: Parallel aur Intersecting Lines · NCERT Ganita Prakash section 5.8–5.9

Seekho

Do lines ke beech aur transversal ke ulte taraf ke angles alternate angles hain: ∠3 aur ∠5, aur ∠4 aur ∠6. ∠6 ke alternate tak pahunchne ke liye uske corresponding ∠2 par jaao, phir ∠2 ke vertically opposite ∠4 par. Dono kadam maap nahi badalte, to ∠6 = ∠4.

∠6 = ∠2 = ∠4

Parallel lines par transversal ke alternate angles hamesha barabar. Udaharan: l ∥ m aur ∠6 = 135°. To ∠2, ∠4, ∠8 = 135° (corresponding aur vertically opposite), aur ∠1, ∠3, ∠5, ∠7 = 180° − 135° = 45°.

Interior angles ek hi taraf ke, jaise ∠3 aur ∠6, lines ke beech t ki usi taraf hain. Parallel lines mein ye milkar 180°: agar ∠3 = 50°, to ∠2 = 130° (linear pair) aur ∠6 = ∠2 = 130°, aur 50° + 130° = 180°. Aur agar ∠2 = 60° par ∠6 = 70°, to lines parallel nahi.

∠3 + ∠6 = 180°

Mudi raah: agar l ∥ m aur raah beech ke bindu P par mude, to P se dono ke parallel line kheencho. Mod do alternate angles mein bat jaata hai, to ∠P = dono angles ka jod. l par 40° aur m par 30° ho to ∠P = 70°. Aur kuch chitra (bhram) aankh ko dhokha dete hain: sach mein parallel lines mudi dikh sakti hain!

∠P = 40° + 30° = 70°

Explore: alternate aur interior angles.

1. m ko tab tak ghumao jab tak alternate angles ∠3 aur ∠5 barabar na hon.
2. Ab interior angles: m ko ∠3 + ∠6 = 180° hone tak ghumao.

Yaad rakho

• Parallel lines mein alternate angles barabar (∠3 = ∠5, ∠4 = ∠6).
• Ek hi taraf ke interior angles milkar 180°.

Quick check

l ∥ m aur ∠4 = 72°. Uska alternate angle ∠6 kitna?

1. 72°
2. 108°
3. 18°
4. 144°

Socho

ABCD mein AB ∥ DC aur AD ∥ BC, ∠D = 60°. ∠A, ∠B aur ∠C kya 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.