Triangle kaise banayein?

Compass kyun kaam aata hai

Maan lo humein aisa triangle chahiye jiski har side 4 cm ho, yaani equilateral triangle. Sirf nishaan waale ruler se hum 4 cm ka base AB kheenchte hain aur phir aisa point C lagaane ki koshish karte hain jo A se 4 cm door ho, aur jaanchte hain ki kya wo B se bhi 4 cm door hai, baar baar. Compass ye andaaza khatam kar deta hai. A se 4 cm door saare points A ke charon taraf 4 cm radius ke circle par hain, aur B se 4 cm door saare points B ke charon taraf ke circle par. Jo point chahiye wo dono par hai, isliye wo wahi hai jahan dono arcs ek doosre ko kaatte hain. Pichhli class ke chapter Playing with Constructions mein ‘ghar’ ka upar ka point bhi isi tarah mila tha.

Teen sides di hon

Yahi tareeka kisi bhi teen sides ke liye chalta hai, jaise 4 cm, 5 cm aur 6 cm.

1. Base AB = 4 cm kheencho.
2. A se 5 cm radius ka arc kheencho, itna lamba ki agle arc ko kaat sake.
3. B se 6 cm radius ka arc kheencho jo pehle arc ko kaate.
4. Kaatne ka point C hai. AC aur BC jodo.

C dono arcs par hai, isliye AC 5 cm aur BC 6 cm hai. Poore circles ki zaroorat nahi, bas itne lambe arcs jo mil sakein. 4, 4, 6 ya 3.5, 3.5, 3.5 jaise triangle bhi isi tarah bante hain; do baraabar sides hon to triangle isosceles hai, aur teen hon to equilateral. Kitaab ke Construct task ke paanch triangles, 4, 4, 6; 3, 4, 5; 1, 5, 5; 4, 6, 8; aur 3.5, 3.5, 3.5, sab isi steps se bante hain, sabse lambi side ko base lekar.

Har teen lambaaiyan kaam nahi karti: agar sabse lambi baaki do ke jod se kam na ho, to arcs kabhi nahi milte. Ye niyam triangle inequality aur angle sum property mein samjhaaya gaya hai.

Do sides aur beech ka angle

Included angle do di gayi sides ke beech ka angle hai. AB = 5 cm, AC = 4 cm aur ∠A = 45° waala ∆ABC banaane ke liye:

1. AB = 5 cm kheencho.
2. A par AB ke saath 45° banaati ek arm kheencho.
3. Us arm par C aisa lagaao ki AC = 4 cm ho.
4. BC jodo.

Is tareeke se 180° se kam har included angle ke liye triangle banta hai; sirf seedha angle ya usse zyaada hone par ye namumkin hai.

Do angles aur beech ki side

Included side wo side hai jo dono diye gaye angles mein saajhi ho. AB = 5 cm, ∠A = 45° aur ∠B = 80° waala ∆ABC banaane ke liye AB kheencho, A par 45° aur B par 80° banaao, aur dono nayi arms C par milti hain. Yahan dono angles ka jod 180° se kam hona chahiye, warna arms nahi milti.

Altitude banaana

A se altitude, A se saamne ki side BC par perpendicular hai. Ise sirf ruler se kheenchna sahi nahi hota, isliye hum set square lete hain: ruler ko BC ke saath rakho, set square ke right angle ki ek edge ruler par tikaao, use tab tak khiskaao jab tak uski khadi edge A ko na chhoo le, aur us edge ke saath line kheencho. Agar triangle B ya C par obtuse ho, to pehle BC ko aage badhaao, kyunki tab altitude triangle ke bahar girta hai.

Ye kyun zaroori hai

Dhyaan se kiye constructions geometry ki baaton ko sahi drawings mein badal dete hain, aur ye vichaar parakhne mein madad karte hain, jaise ki triangle ban bhi sakta hai ya nahi. In constructions se bane triangles ke prakaar triangles ke types mein hain. Har sawaal ke jawaab Chapter 7 ke NCERT solutions mein hain; poore Chapter 7 ke notes bhi dekho.