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Isosceles aur Samabahu Tribhuj ke Angles

Class 7 Maths · Chapter 9: Jyamitiya Judwaan · NCERT Ganita Prakash section P2 1.3

Seekho

△ABC lo jismein AB = AC aur ∠A = 80°. BC par altitude AD kheencho. Ab △ADB aur △ADC mein D par right angle, barabar hypotenuse AB = AC, aur saajhi bhuja AD: RHS se sarvangsam. To ∠B = ∠C.

AB = AC → ∠B = ∠C

Isosceles tribhuj mein barabar bhujaon ke saamne ke angles barabar. ∠A = 80° par ∠B + ∠C = 100°, to har ek 50°. Ulta, agar barabar angles 35° ke hain, to teesra 180° − 70° = 110°.

(180° − 80°) ÷ 2 = 50°

Samabahu tribhuj: AB = AC se ∠B = ∠C, aur AB = BC se ∠A = ∠C. To teeno angles barabar, aur jod 180°, to har ek 60°. Ye humne sirf sarvangsamta se paaya, bina naape!

3 × 60° = 180°

Vritt mein: agar A kendra aur B, C vritt par, to AB aur AC dono radius, to △ABC isosceles. ∠A = 120° par ∠B aur ∠C har ek 30°. Sarvangsam tribhuj har jagah: Howrah ke Rabindra Setu jaise pulon mein, gumbadon, pyramidon aur rangoli mein.

(180° − 120°) ÷ 2 = 30°

Explore: isosceles angles.

  1. AB = AC aur ∠A = 80°. Angle ko ∠B tak kholo.
  2. Angle ko samabahu tribhuj ke ek angle tak kholo.
  3. A vritt ka kendra; B, C us par; ∠A = 120°. ∠B tak kholo.

Yaad rakho

  • Barabar bhujaon ke saamne ke angles barabar.
  • Samabahu tribhuj ka har angle 60°.

Quick check

△PQR mein PQ = PR aur ∠Q = 70°. ∠P kitna?

  1. 40°
  2. 70°
  3. 55°
  4. 110°
Answer

40°. ∠R = ∠Q = 70°, to ∠P = 180° − 140° = 40°.

Socho

Kya ulta bhi sach hai: agar tribhuj mein ∠B = ∠C, to kya AB = AC?

Ek answer

Haan. Altitude AD giraao: do chhote tribhujon mein ∠B = ∠C, D par right angle aur saajhi AD, to sarvangsam (AAS). Isliye AB = AC.

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.