Triangles ke types
Short mein jawab
Triangles ko sides aur angles ke hisaab se baanta jaata hai. Sides ke hisaab se equilateral triangle ki teen sides baraabar hoti hain, isosceles ki do aur scalene ki koi nahi. Angles ke hisaab se acute-angled ke saare angles 90° se kam, right-angled ka ek angle 90° aur obtuse-angled ka ek angle 90° se zyaada hota hai.
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Triangles ko baantne ke do tareeke
Triangles banaate hue hum kai aakritiyan dekhte hain: lambe aur patle, chaude aur chapte, ekdum niyamit ya tedhe medhe. Do saral sawaal inhe baant dete hain. Kya koi sides baraabar hain? Aur sabse bada angle kitna bada hai?
Sides ke hisaab se
- Equilateral triangle ki teeno sides baraabar hoti hain. Ye sabse symmetric triangle hai, aur iska har angle 60° hai.
- Isosceles triangle ki do sides baraabar hoti hain, jaise 4 cm, 4 cm aur 6 cm.
- Scalene triangle ki teeno sides alag lambaai ki hoti hain, jaise 4 cm, 6 cm aur 8 cm.
Circles se isosceles triangles jaldi bante hain. Kisi circle ke centre ko us par ke kinhi do points se jodo: do sides radii hain, isliye baraabar hain. Agar do baraabar circles ek doosre ke centres, A aur B, se guzarte hon, to dono centres aur circles ke milne ka koi bhi point equilateral triangle banaate hain.
Angles ke hisaab se
- Acute-angled triangle ke teeno angles acute, yaani 90° se kam, hote hain.
- Right-angled triangle, yaani right triangle, ka ek angle right angle hota hai.
- Obtuse-angled triangle ka ek angle obtuse, yaani 90° se zyaada, hota hai.
Pehle type mein teeno angles acute kyun hone chahiye? Kyunki har triangle ke teeno angles ka jod 180° hai, isliye har triangle mein pehle se kam se kam do acute angles hote hain. Kisi triangle mein do right angles ya do obtuse angles bhi nahi ho sakte.
Isliye angles ke hisaab se triangle ka naam rakhne ke liye bas uska sabse bada angle dekho. Sabse bada angle 90° se kam ho to triangle acute-angled hai; theek 90° ho to right-angled; aur 90° se zyaada ho to obtuse-angled. 50°, 60° aur 70° angles waala triangle acute-angled hai, 30°, 60° aur 90° waala right-angled, aur 120°, 30° aur 30° waala obtuse-angled.
Altitudes aur right triangles
Kisi vertex ki height altitude ke saath naapi jaati hai, yaani us vertex se saamne ki side par perpendicular. Acute-angled triangle mein teeno altitudes andar girte hain. Obtuse-angled triangle mein saamne ki side ko aage badhaana padta hai aur altitude triangle ke bahar girta hai. Right-angled triangle mein ek khaas baat hoti hai: right angle banaane waali do sides khud altitudes hain, kyunki har ek doosri par perpendicular hai.
Kaunse mel mumkin hain?
Baantne ke dono tareeke saath mila sakte hain. Equilateral triangle hamesha acute-angled hai, kyunki uska har angle 60° hai; wo kabhi right-angled ya obtuse-angled nahi ho sakta. Isosceles triangle right-angled ho sakta hai, 90°, 45° aur 45° angles ke saath, ya obtuse-angled, jaise 120°, 30° aur 30° angles ke saath. Scalene triangle teeno angle types mein se koi bhi ho sakta hai, jaise 3, 4, 5 waala triangle, jisme ek right angle hai.
Ye kyun zaroori hai
Sides aur angles se triangles ka naam rakhna aakritiyon ko theek theek bataane aur unke gunon ka andaaza lagaane mein madad karta hai: equilateral triangle ke angles hamesha 60° hain, aur right triangle apne do altitudes khud liye chalta hai. Ye triangles kaise kheenchein, ye triangle kaise banayein mein hai, aur kai baaton ke peeche ka 180° waala niyam triangle inequality aur angle sum property mein. Har sawaal ke jawaab Chapter 7 ke NCERT solutions mein hain; poore Chapter 7 ke notes bhi dekho.
Practice karo
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Kisi triangle ki sides 5 cm, 5 cm aur 8 cm hain. Sides ke hisaab se ye kis type ka hai?
Jawab dekho
Jawab: (b) Isosceles
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Kisi triangle ke angles 30°, 60° aur 90° hain. Angles ke hisaab se ye kis type ka hai?
Jawab dekho
Jawab: (b) Right-angled
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Kis triangle mein altitude triangle ke bahar gir sakta hai?
Jawab dekho
Jawab: (c) Obtuse-angled
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Kya koi triangle isosceles aur right-angled dono ho sakta hai? Udaaharan do.
Jawab dekho
Jawab: Haan. 90°, 45° aur 45° angles waale triangle ki do sides baraabar hain, wahi do sides jo right angle banaati hain.
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Acute-angled triangle ke teeno angles acute kyun hone chahiye?
Jawab dekho
Jawab: Kyunki har triangle mein pehle se kam se kam do acute angles hote hain (teeno ka jod 180° hai), to ‘ek acute angle’ har triangle par laagu ho jaata; ye naam unhi triangles ke liye hai jinka sabse bada angle bhi acute ho.
Students ke sawal
Sides ke hisaab se triangles ke types kya hain?
Equilateral triangle ki teeno sides baraabar hoti hain, isosceles triangle ki do sides baraabar hoti hain, aur scalene triangle ki teeno sides alag lambaai ki hoti hain. Equilateral triangle sabse symmetric hai; 4, 4, 6 jaisa triangle isosceles aur 4, 6, 8 jaisa scalene hai.
Angles ke hisaab se triangles ke types kya hain?
Acute-angled triangle ke teeno angles 90° se kam hote hain, right-angled triangle ka ek angle theek 90° hota hai, aur obtuse-angled triangle ka ek angle 90° se zyaada hota hai. Kisi triangle mein do right ya do obtuse angles nahi ho sakte, kyunki teeno angles ka jod bas 180° hai.
Triangle ka altitude kya hota hai?
Altitude kisi vertex se saamne ki side par, ya us side ko aage badhaakar, daala gaya perpendicular segment hai. Iski lambaai us vertex ki height hai. Har triangle ke teen altitudes hote hain; obtuse-angled triangle mein unme se do bahar girte hain, aur right-angled triangle mein right angle banaane waali do sides khud altitudes hain.
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