Triangle Angle Sum Theorem Proof

The Theorem states that the sum of all the three angles of a triangle is always equal to 180 degrees.

Triangle Angle Sum Theorem

Statement:
  A triangle with the interior angles MNS.

To prove:

Diagram



Construction:


Proof:


MN is a transversal.


Similarly,
--->(2)

(is a straight line and sum of the angles at M is equal to 180.

From (1) and (2), We get


The measure of interior angles of a triangle or the two right angles are equal to 180 degrees.
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