prove that sum of the three angle of a triangle is 180°
Answers
Answer:
ANSWER
Given :
A triangle ABC.
To prove :
∠A+∠B+∠C=180
o
⟹∠1+∠2+∠3=180
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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
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Thus, the sum of three angles of a triangle is 180
o
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hope it helps.....
Answer
To prove :-
Sum of all angles of a triangle is 180°
Construction :-
Through A,draw a line DAE || BC
Proof :-
→ DAE || BC and AB is the transversal.
→ ∠4 = ∠2 [ alternate interior angle ]
DAE || BC and AC is transversal.
→ ∠5 = ∠3 [ alternate interior angle ]
Now,DAE is a straight line.
→ ∠4 + ∠1 + ∠5 = 180° [ angles on the same side of DAE at point A ]
→ ∠1 + ∠4 + ∠5 = 180°
→ ∠1 + ∠2 + ∠3 = 180° [ °.°∠4 = ∠2 and ∠5 = ∠3]
Hence,sum of the angles of a triangle is 180°.
Note :- See the attachment for diagram.
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Remarks :-
A triangle cannot have more than one right angle.
A triangle cannot have more than one obtuse angle.
In a right angle triangle,the sum of two acute angles is 90°.
hope it will help you