Question

3. Theorem : The sum of the angles of a triangle is 180°
step by step​

Answer 1

Step-by-step explanation:

Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof: ... To prove the above property of triangles, draw a line \overleftrightarrow {PQ} parallel to the side BC of the given triangle.

Answer 2

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 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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