Question

state a prove angle sum property of a triangle​

Answer 1

Answer:

To prove the above property of triangles, draw a line \overleftrightarrow {PQ} parallel to the side BC of the given triangle. Thus, the sum of the interior angles of a triangle is 180°.

Step-by-step explanation:

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Answer 2

Angle Sum Property:

→ Sum of all angles in a triangle is always 180°

Given:

• ΔABC

To prove:

⟶ ∠ABC + ∠BAC + ∠ACB = 180°

Construction:

Draw PQ || BC

Method:

Since PQ || BC,

By Alternate Interior Angles,

• ∠PAB = ∠ABC
• ∠QAC = ∠ACB

Now consider the straight line PAQ.

By Linear Pair of Angles,

∠PAB + ∠BAC + ∠QAC = 180°

Substitute

∠PAB as ∠ABC and

∠QAC as ∠ACB.

We get

∠ABC + ∠BAC + ∠ACB = 180°

★ Hence Proved ★

Know More:

1. Alternate Interior Angles states that when a transversal cuts 2 parallel lines, then the angles on the either side of the transversal are equal.
2. Linear Pair of Angles states that sum of all angles on a straight line sum up to 180°