Prove that the sum of the angles of a triangle is 180
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Answer:
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 1 ∥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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Answer:
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