Question

prove angle sum property of triangle

Answer 1

Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Proof: Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→PQ↔parallel to the side BC of the given triangle.



 

Since PQ is a straight line, it can be concluded that:

∠PAB + ∠BAC + ∠QAC = 180°  ………(1)

SincePQ||BC and AB, AC are transversals,

Therefore, ∠QAC = ∠ACB (a pair of alternate angle)

Also, ∠PAB = ∠CBA (a pair of alternate angle)

Substituting the value of ∠QAC and∠PAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of the interior angles of a triangle is 180°.

Answer 2

Let ABC be a triangle.
Draw PQ parallel to BC.

Now,
∠1 +∠2 +∠3=180°..................... (i)

∠B = ∠1 [Alternate interior angles]
∠C= ∠3 [Alternate interior angles]


Substituting, ∠1 = ∠B and ∠3= ∠C;We have
∠B+ ∠2+ ∠C=180°
∠B +∠A +∠C=180°


Hence, angle sum property of triangle is proved.