Rectangle aur square kaise banayein

Koi figure rectangle ya square kab hai?

Rectangle ABCD mein A, B, C aur D uske corners hain, AB, BC, CD aur DA uski sides, aur ∠A, ∠B, ∠C aur ∠D uske angles. AB aur CD ek doosre ke saamne hain, isliye ye aamne-saamne ki sides hain; AD aur BC doosri jodi hai.

Rectangle ki do properties:

• R1: aamne-saamne ki sides lambai mein barabar hoti hain, aur
• R2: saare angles 90° hote hain.

Square ki do properties:

• S1: saari sides barabar hoti hain, aur
• S2: saare angles 90° hote hain.

Square mein R1 aur R2 bhi hote hain, isliye har square ek rectangle bhi hai.

Rectangle ka naam kaise likhein

Naam mein corners figure ke chaaron taraf ghoomne ke kram mein likhte hain, kisi bhi corner se shuru karke, kisi bhi disha mein. Rectangle ABCD ko BCDA, CDAB, DABC, ADCB, DCBA, CBAD ya BADC bhi keh sakte hain. ABDC naam nahi hai, kyunki B se D side ke saath nahi, rectangle ke aar-paar jaata hai.

Ghumaye hue square aur rectangle

Square kaagaz ko itna ghumao ki wo ek corner pe khada ho jaaye. Uski sides ab bhi barabar hain aur angles ab bhi 90° hain, isliye wo ab bhi square hai. Isi tarah ghumaya hua rectangle bhi rectangle hi hai. Dot paper pe ghumayi hui figure bina instruments ke check kar sakte ho: agar har side utne hi dots aage aur neeche jaati hai, bas ghumi hui, to sides barabar hain.

6 cm side ka square banane ke steps

1. Ruler se PQ = 6 cm kheencho.
2. P se PQ ke perpendicular ek line kheencho.
3. Compass ko 6 cm kholo. Needle P pe rakh ke perpendicular ko S pe kaato, taaki PS = 6 cm ho. PS 6 cm hi hona chahiye kyunki square ki saari sides barabar hoti hain.
4. Q se PQ ke perpendicular ek line kheencho.
5. Wahi khulaav rakh ke needle Q pe rakho aur is line ko R pe kaato.
6. SR jodo.

Ab naapo: RS 6 cm hai, aur ∠R aur ∠S 90° hain. Square ki dono properties poori hain, isliye PQRS square hai.

Di gayi sides se rectangle banana

4 cm aur 6 cm sides wale rectangle ke liye AB = 6 cm kheencho, A aur B pe perpendicular kheencho, un par 4 cm pe D aur C mark karo, aur DC jodo. R1 check karo: AB = DC = 6 cm aur AD = BC = 4 cm. R2 check karo: chaaron angles 90° hain. Lamba patla rectangle, jaise 2 cm by 10 cm, bhi bilkul isi tarah banta hai.

Kya aisi 4 sides wali figure ban sakti hai jiske saare angles 90° hon par aamne-saamne ki sides barabar na hon? Koshish karo. Jab A aur B pe angles 90° hain, to A aur B se sides seedhe upar jaati hain. Agar ek doosri se chhoti ho, to upar wali side tirchhi ho jaati hai aur upar ke angles 90° nahi rehte. Isliye ye nahi ho sakta: chaar right angles aamne-saamne ki sides ko barabar bana dete hain.

Side aur diagonal se rectangle banana

Diagonal aamne-saamne ke do corners ko jodta hai. Ek side 5 cm aur diagonal 7 cm wala rectangle banane ke liye pehle rough diagram banao, phir:

1. DC = 5 cm kheencho.
2. C se DC ke perpendicular ek line l kheencho. Corner B kahin is l pe hai.
3. B, D se 7 cm door bhi hai. D se 7 cm door saare points D ke chaaron taraf 7 cm radius ke circle pe hain, isliye D ko centre maan ke 7 cm radius ka arc kheencho. Jahan ye l ko kaate, wahi B hai. Trial and error ki zaroorat nahi.
4. D pe DC ke aur B pe BC ke perpendicular kheencho. Ye A pe milte hain.

Check karo ki ABCD mein rectangle ki dono properties hain. Uski doosri side BC lagbhag 4.9 cm aati hai.

Squares se bane rectangle

Jo rectangle 2 ek jaise squares mein kat sake, uski lambi side chhoti side ki theek 2 guna honi chahiye, jaise 4 cm by 8 cm. Use bina do baar naape banane ke liye chhoti side kheencho, uske ek sire pe perpendicular kheencho, aur compass se chhoti side ko perpendicular pe do baar copy karo. 3 ek jaise squares ke liye teen baar copy karo.

Chapter ke har construction ke jawab Chapter 8 ke NCERT solutions mein hain.