Theorem: Sum of the Angles of a Triangle

Sum of the angles of a triangle is equal to two right angles, i.e., 180 degrees

ABC is a triangle

To Prove

A + B + ACB = 180^o

Produce BC to D. Through C draw CE || BA.

Proof of Sum of the Angles of a Triangle:

Corollary of Theorem on Sum of the Angles of a Triangle

If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles.

In ABC, BC is produced to D.

To Prove Corollary of Sum of Angles of Triangle:

If in a triangle ABC, the bisectors of the angles ABC and ACB meet at M, prove that

(Sum of angles of a D = 180^o)

Also ( MB bisects )

( MC bisects )

…(1)

In

(Sum of the angles of a = 180^o)

Using (1)

BMC = 180^O - (CBM + BCM)

or (Proved)