Question

Q.26 Prove" The sum of the angles of a triangle is 180°.​

Answer 1

Theorem : Angel sum property of triangle.

Statement : The sum of the angles of a triangle is 180°

Given : ABC is a triangle with angle ∠B , ∠A

To prove : ∠A+ ∠B + ∠C = 180°

Construction: Though A draw a line PQ||BC

Proof : PQ||BC (by construction)

and AB is transversal

∠1 = ∠B (Alternate interior angle) ------- 1

similarly AC is a transversal and PQ||BC

=> ∠2+ ∠c (alternate interior angle)--------2

PAQ is straight line

∠1 + ∠2 + ∠3 = 180°

∠B+ ∠A + ∠C = 180° (from 1 & 2)

∠A + ∠B + ∠C = 180°

Hence , the sum of the angles of a triangle is 180° .

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