## Friday, July 27, 2012

### Exterior Angle Sum Property of a Triangle

A triangle has three corners, called vertices. The sides of a triangle that come together at a vertex form an angle. This angle is called the interior angle. In the figure below, the angles a,b and c are the three interior angles of the triangle. We know that the sum of interior angles of a triangle is 180°. You may visit the  links http://mathematicsbhilai.blogspot.in/2012/01/triangle-angle-sum-property-ii.html  and http://mathematicsbhilai.blogspot.in/2011/05/triangle-angle-sum.html

An exterior angle is formed by extending one of the sides of the triangle; the angle between the extended side and the other side is the exterior angle. In the figure, angle d is an exterior angle.
In the above figure ∠ACD is an exterior angle of Δ ABC.

Because ∠a +∠b +∠c = 180°, and ∠b +∠d = 180°, we can see that that ∠d =∠a +∠c. This is stated as a theorem.  An exterior angle of a triangle is equal to the sum of the two opposite (nonadjacent) interior angles. This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com