how do we use the triangle sum conjecture?

 

How Do We Use the Triangle Sum Conjecture?

 

 

 

A conjecture is the sum of measures of the angles in every triangle is 180 degrees. Using the conjecture involves using alternate interior angles to determine the other angles meausres.

 

 

Examples:

 



 

http://www.geom.uiuc.edu/~dwiggins/conj04.html

 

In the example, angles A,B, and C in triangle ABC all equal to 180 degrees. The angle measures can also be determined by alternate interior angles:

 

 

 

 

http://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t285.htm

 

 

 

This example shows a triangle abc underneath line segment DE. A is the midpoint of line DE. The alternate interior angles are a and b because they're not only supplementary to the line segment, but aslo a linear pair of angles.