How to prove that the sum of the angles of a triangle is equal to 180°. (prove that in a practical way)
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Answer:Angles B and B' are corresponding angles, ... So, the angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'. The three angles A', B', and C' form together a straight angle (they are along the line l). So, their angle sum is 180°.
Step-by-step explanation:
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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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