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Rectangles aur Squares ke Diagonals

Class 6 Maths · Chapter 8: Constructions se Khel · NCERT Ganita Prakash section 8.5

Seekho

Aamne-saamne ke konon ko jodne wali line diagonal hai. Rectangle ABCD ke do hain: AC aur BD. Nisha apni copy ke cover par dono naapti hai: 25 cm aur 25 cm. Rectangle ke dono diagonals hamesha barabar hote hain.

Diagonals beech mein ek point O par kat-te hain. O har diagonal ko aadha-aadha kaat-ta hai: OA = OC aur OB = OD. To chaaron, OA, OB, OC aur OD, barabar hain!

OA = OB = OC = OD

Isse ek badhiya construction milta hai: do barabar lines banao jo ek doosre ko aadha kaatein, aur unke sire jodo. Hamesha rectangle banega! Isi tarah ek bhuja aur ek diagonal se rectangle banta hai.

Square mein diagonals ek aur kaam karte hain: wo right angle (90°) par kat-te hain. Lambe patle rectangle mein wo tirchhe kat-te hain.

Explore: rectangle badlo aur uske diagonals dekho.

  1. 8 cm × 6 cm ka rectangle banao. Har diagonal kitna lamba hai?
  2. Diagonals ko right angle par kaato.
  3. Aisa rectangle banao jiske diagonals 5 cm lambe hon.

Yaad rakho

  • Rectangle ke diagonals barabar hote hain aur ek doosre ko aadha kaat-te hain.
  • Square ke diagonals 90° par bhi kat-te hain.

Quick check

Rectangle PQRS mein diagonals O par kat-te hain, aur PR = 12 cm. OQ kitna lamba hai?

  1. 6 cm
  2. 12 cm
  3. 24 cm
  4. 3 cm
Answer

6 cm. QS = PR = 12 cm, aur O use aadha kaat-ta hai: OQ = 6 cm.

Socho

Rohan do lines banata hai, har ek 6 cm, jo apne beech ke point par 90° par kat-ti hain. Wo chaaron sire jodta hai. Kaunsi shape milti hai?

Ek answer

Square. Lines barabar hain aur ek doosre ko aadha kaat-ti hain, isliye shape rectangle hai; aur 90° par kat-ti hain, isliye square.

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.