Question

state and prove angles sum property of a triangle ​

Answer 1

Answer:

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

Proof for Angle Sum Property of a 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

Angle Sum property of a triangle states that All the angles of any triangle will add up to 180 °

Given - ABC is a triangle

To prove that Angle A +B+C =180°

Prove -

Draw a line Parallel to BC passing through A

Angle 1 =Angle B (alternate interior angle). -----(a)

Angle 3 = Angle C (Alternate interior angle)--------(b)

Now

Angle 1 + A+2 =180° (linear pair)

From (a) and (b)

Angle B +A+C = 180°

Hence All angle of a triangle is equal to 180°.....

Hope it helps:-D