Prove that the sum of the internal angles of a triangle is 180°.
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Prove that the sum of the internal angles of a triangle is 180°.
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Prove that the sum of angles of a triangle is 180
∘
.
Let a triangle ABC and draw a line l through A and parallel to the base BC.
∵BC∥l and AB and AC are transversals on it.
∴∠4=∠2…(i) (Alternate angles)
and ∠5=∠3…(ii) (Alternate angles)
Adding equations (i) and (ii), we get
∠4+∠5=∠2+∠3
Add ∠1 on both sides.
⇒∠1+∠4+∠5=∠1+∠2+∠3…(iii)
∠1+∠4+∠5=180
∘
(∵l is a straight line)
From (iii),
∠1+∠2+∠3=180
∘
Hence, sum of angles of a triangle is 180
∘
.
Hence Proved.
the sum of The triangle is 180