Question

State and prove the Theorem on the Angle Sum Property of a Triangle.​

Answer 1

Answer:

• Construction: Draw a line PQ parallel to side BC of the given triangle and passing through point A. Thus, the sum of the interior angles of a triangle is 180°. Theorem: If any one side of a triangle is produced then the exterior angle so formed is equal to the sum of two interior opposite angles.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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←→ parallel to the side BC of the given triangle.

Angle sum property of a triangle theorem 1

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

∠PAB + ∠BAC + ∠QAC = 180° ………(1)

Since PQ||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°.

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