(42) Prove that the sum of the angles of a triangle is 180°
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EXPLANATION.
Sum of the angles of a triangle = 180°.
As we know that,
To prove.
⇒ ∠1 + ∠2 + ∠3 = 180°.
Construction.
Draw a line m & n passing through A parallel to BC.
Proof.
As we know that,
⇒ ∠2 = ∠4. [ Alternate angles are equal.]
⇒ ∠3 = ∠5. [ Alternate angles are equal.]
We can write.
⇒ ∠1 + ∠4 + ∠5 = 180°.
⇒ ∠1 + ∠2 + ∠3 = 180°.
Hence proved.
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Step-by-step explanation:
Sum of the angles of a triangle = 180°.
As we know that,
To prove.
⇒ ∠1 + ∠2 + ∠3 = 180°.
Construction.
Draw a line m & n passing through A parallel to BC.
Proof.
As we know that,
⇒ ∠2 = ∠4. [ Alternate angles are equal.]
⇒ ∠3 = ∠5. [ Alternate angles are equal.]
We can write.
⇒ ∠1 + ∠4 + ∠5 = 180°.
⇒ ∠1 + ∠2 + ∠3 = 180°.
Hence proved.
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