Prove that sum of the angles of triangle is 180 degrees

Hello friends !! Aaj mai aapko bataunga ki , How to prove that the sum of the angles of triangle is 180 degrees ? Matlab hum kaise sidh kar sakte hai ki , tribhuj ke tino kono ka yogphal 180 degrees hota hai ?
Aaj ka jo topic hai wo ek theorem hai and I think iss theorem ko class-9th or 10th me hume padaya jata hai. Ye theorem bahot hi jadaya important bhi hai. To mai aapko aaj issi topic ke baare me details me batane jaa raha hu.

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Ab mai aapko bata deta hu ki aaj hum kya-kya shikhane waale hai ?
Aaj hum jaanenge ki ,
• Ye theorem kya kahata hai ?
• Iss theorem ko hum proof kaise karte hai ?
To aayiye ek-ek kark start karte hai.

Chaliye sabse pahle hum jaan lete hai ki -:

• Ye theorem kya kahata hai ?

Theorem-: Sum of the angles of triangle is 180 degrees .

Ye theorem kahata hai ki , kisi bhi triangle ke sabhi angles ( 3 angles ) ko agar hum add (+) kare to humesha hume addition result 180° hi milega.

For example-: Niche diye figure-1 me ∆ABC ko dhyaan se dekiye.

Figure-1

Fig-1 ki help se , Ye theorem kahata hai ki ,
/_A + /_B + /_C = 180°

I hope ki aap theorem ka matalab samjh gaye honge. Ab hum isko proof karna shikh lete hai.

• Iss theorem ko hum proof kaise karte hai ?
To aayiye fig-1 ki help se iss theorem ko proof karna start karte hai.

Proof -: Diya hai -: Ek ∆ABC
Sidh karna hai -:

/_A+/_B+/_C = 180°

Sabse pahle hum ∆ABC ke point A par ek line draw karenge. Ye line , triangle ABC ke side BC ke parallel (samantar) hona chahiye. Iss line par 2 point D aur E lenge.
Saath hi saath hum line BC ke point B aur C se line ko thoda aage badayenge.
(See the figure-2)

Figure-2

Ab aap figure-2 me dekh sakte hai ki , total 5 angle ban raha hai. Jo iss prakar hai -:

/_DAB = /_1
/_BAC = /_2
/_CAE = /_3
/_ABC = /_4 aur
/_ACB = /_5
Saath me /_DAE = straight angle hai. Aur hum jaante hai ki straight angle ka maan 180° hota hai.
To iss karan /_DAE = 180°
Figure-2 me dekh sakte hai ki ,
/_DAE = /_DAB+/_BAC+/_CAE
➨ 180° = /_DAB+/_BAC+/_CAE
➨ /_DAB+/_BAC+/_CAE = 180°
Or , /_1+/_2+/_3 = 180° .....(i)

Ab /_DAB = /_CBA
Or , /_1 = /_4 ........(ii)
and /_EAC = /_ACB
/_3 = /_5 ......(iii)

Kyuki ye sabhi angle alternate angles hai.
Ab eq(ii) and (iii) ki value eq(i) me rakhane par -:
/_CBA+/_BAC+/_ACB = 180°
➨ /_B+/_A+/_C = 180°
Or , /_A+/_B+/_C = 180° proved

To humne prove kar diya ki triangle ke 3 angles ka sum 180° hota hai.
I hope ki aapko ye proof samjh aaya hoga. Iss proof ko samjhne me agar aapko kisi bhi jagah par koi bhi doubt ya problem ho rahi ho to aap hume comment kark puchh sakte hai.Hum aapki puri help karne ki koshish karenge.

Agar aapko aaj ka topic pasand aaya ho to please apne friends ke saath facebook , Whatsapp , Google+ etc. par share kark humari help kare.
Hum issi tarah se mathematics se related topic yaha par share karte rahate hai.
Aap kis mathematics topic ke baare me jaanana chahte hai ? Niche comment box me comment kark bataye. Hum uss topic ke baare me aapko complete article likh kar details me batayege.
Thanks for reading !!!