01 · TRIANGLE ANGLE SUM
Sum of Angles is 180°
Theorem: The sum of the angles of a triangle is 180° (∠A + ∠B + ∠C = 180°).
PROOF PROCEDURE
Proof of Angle Sum Theorem
1. Consider △ABC. Draw a line XAY parallel to BC passing through vertex A.
2. Since XAY is a straight line, ∠XAB + ∠BAC + ∠YAC = 180° (Line angle sum).
3. Since XAY ∥ BC, alternate interior angles are equal: ∠XAB = ∠B and ∠YAC = ∠C.
4. Substituting these gives ∠B + ∠A + ∠C = 180°.
02 · EXTERIOR ANGLE THEOREM
Exterior Angle of a Triangle
If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.