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Tribhujon ki Sarvangsamta

Class 7 Maths · Chapter 9: Jyamitiya Judwaan · NCERT Ganita Prakash section P2 1.2

Seekho

Meher aur Kabir ko ek bada tribhujaakaar dhaancha copy karna hai. Ve bhujaayein naapte hain: 40, 60 aur 80 cm. Kya angles bhi chahiye? Compass se 4, 6, 8 cm tribhuj banaane par chaap aadhaar ke upar aur neeche do binduon par kaat'te hain, par dono tribhuj darpan-roop: sarvangsam! To barabar bhujaayein kaafi: SSS niyam.

SSS: three sides equal → congruent

Sarvangsamta likhna: △ABC ≅ △XYZ ka matlab A ↔ X, B ↔ Y, C ↔ Z (pehla pehle se, doosra doosre se, teesra teesre se). Tab AB = XY, BC = YZ, AC = XZ aur ∠A = ∠X, ∠B = ∠Y, ∠C = ∠Z. △ACB ≅ △XZY wahi kehta hai, par △ACB ≅ △XYZ galat hai.

△ABC ≅ △XYZ: A↔X, B↔Y, C↔Z

Aur kya chalta hai? Sirf barabar angles nahi (wahi aakaar, alag maap). Do bhujaayein aur unke beech ka angle (SAS) chalta hai; do angles aur unke beech ki bhuja (ASA) chalta hai. Do angles aur beech se bahar ki bhuja (AAS) bhi: angle jod se teesra angle milta hai, phir ASA.

SSS · SAS · ASA · AAS · RHS

SSA nahi chalta: PQ = 6 cm, ∠P = 30° aur QR = 4 cm ke saath, Q se 4 cm ka chaap 30° wali line ko do binduon par kaat'ta hai, do alag tribhuj. Par right tribhujon mein chalta hai: right angle, hypotenuse (right angle ke saamne ki bhuja) aur ek aur bhuja barabar ho to sarvangsam: RHS.

Sarvangsamta ka upyog: agar O, AD aur BC dono ka madhya-bindu hai, to AO = OD, BO = OC, aur O par vertically opposite angles barabar. SAS se △AOB ≅ △DOC, to AB = DC. Aayat ABCD mein vikarn BD se △ABD ≅ △CDB (SSS, BD saajha).

Explore: kaafi ya nahi?

  1. Niyamon ko sort karo.

Yaad rakho

  • SSS, SAS, ASA, AAS aur RHS sarvangsamta pakki karte hain; AAA aur SSA nahi.
  • △ABC ≅ △XYZ mein ek hi sthaan ke akshar sangat hain.

Quick check

△SUN ≅ △BOX. UN ke barabar kaunsi bhuja?

  1. OX
  2. BO
  3. BX
  4. SU
Answer

OX. U ↔ O aur N ↔ X, to UN = OX.

Socho

△HEN ≅ △BIG. Ise kehne ke do aur sahi tareeke likho.

Ek answer

Dono naamon par ek hi badlaav: △EHN ≅ △IBG, △NEH ≅ △GIB, △HNE ≅ △BGI, △ENH ≅ △IGB, △NHE ≅ △GBI.

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.