A plane figure bounded by three lines in a plane is called a triangle. The figure below represents a ΔABC, with AB, AC andBC as the three line segments.

A triangle (denoted by the symbol △) is the simplest closed shape in geometry. It is a two-dimensional figure made by connecting three points that do not lie on the same straight line (non-collinear).

Angle Sum Property of a Triangle:

Theorem: The sum of the angles of a triangle is 180°.

Construction: Draw a line XPY parallel to QR through the opposite vertex P.

Proof:

In △ PQR,
Sum of all angles of a triangle is 180°.
∠PQR + ∠PRQ + ∠QPR = 180°......(1)

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

Therefore, ∠XPY + ∠QRP + ∠RPY = 180°.

But XPY || QR and PQ, PR are transversals.

So,
∠XPY = ∠PQR.....(Pairs of alternate angles)

∠RPY = ∠PRQ.....(Pairs of alternate angles)

Substituting ∠XPY and ∠RPY in (1), we get

∠PQR + ∠PRQ + ∠QPR = 180°

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