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.