Question

State and prove the angle sum property of a triangle.
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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 \overleftrightarrow {PQ} parallel to the side BC of the given triangle

Answer 2

Answer:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof: ... Thus, the sum of the interior angles of a triangle is 180°.

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°.