Prove that the sum of all angles of a triangle is 180 degree
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Step-by-step explanation:
Hey mate here is your answer:
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Given :
A triangle ABC.
To prove :
∠A+∠B+∠C=180°
⟹∠1+∠2+∠3=180°
Construction :
Through A, draw a line l parallel to BC.
Proof :
Since l∥BC. Therefore,
∠2=∠4 .......eq(i)
And, ∠3=∠5......eq(ii)
adding eq(i)and(ii)
Therefore, ∠2+∠3=∠4+∠5
∠1+∠2+∠3=∠1+∠4+∠5 [adding∠1bothSide]
∠1+∠2+∠3=180°
Thus, the sum of three angles of a triangle is 180°.
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Hope it helps you.
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Answered by
2
Given :
A triangle ABC.
To prove :
∠A+∠B+∠C=180
o
⟹∠1+∠2+∠3=180
o
Construction :
Through A, draw a line l parallel to BC.
Proof :
Since l∥BC. Therefore,
∠2=∠4 .......eq(i)
And, ∠3=∠5......eq(ii)
adding eq(i)and(ii)
Therefore, ∠2+∠3=∠4+∠5
∠1+∠2+∠3=∠1+∠4+∠5 [adding∠1bothSide]
∠1+∠2+∠3=180
Thus, the sum of three angles of a triangle is 180
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