Properties of Triangles:

a. Angle Sum Property

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

Proof:

Given:

To Prove:

First draw a line parallel to .

are the transversals.

Since ,

(Alternate Angles)……………………….i)

Similarly,

(Alternate Angles)…………………………ii)

Adding i) and ii), we get

…………………………iii)

Adding on both sides of iii) we get the following

Since (Angles on a straight line)

Hence

or

b. Exterior Angle Property

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

Proof:

To Prove:

Given: Given:

Extend . Also draw a like are the transversals.

Therefore, (Alternate Angles)

Similarly, (Corresponding Angles)

or

Hence proved, that if one side of the triangle is produced, then the exterior angle so formed is equal to the sum of the interior opposite angles.