MemberJune 22, 2023 at 5:36 pm::
The sum of all interior angles of a triangle is always 180 degrees. This property holds true for all triangles, regardless of their shape or size.
Proof of ANGLE SUM PROPERTY THEOREM:
Step 1: Draw a line AB through the vertex P and parallel to the side QR of a triangle PQR.
Step 2: ∠APQ + ∠QPR + ∠RPB = 180 degrees
[Linear Pair theorem] -(1)
Step 3: ∠APQ = ∠PQR [Alternate interior angles] -(2)
Step 4: ∠RPB = ∠PRQ [Alternate interior angles] -(3)
Step 5: Substituting equation (2) and (3) in equation
Thus, the theorem is proved.