Angle Sum Theorem
The Angle Sum Theorem gives an important result about triangles, which is used in many algebra and geometry problems. We give the proof below.
Theorem: The sum of the measures of the interior angles of a triangle is 180°.
Given: ΔXYZ
Prove: m
1 + m2 + m3 = 180°
| Statements | Reasons |
Construct a line parallel to |
Construction |
| m1 + m5 = mAYX |
Angle Addition Postulate |
| mAYX + m4 = 180° |
Linear Pair Postulate |
| m1 + m5 + m4 = 180° |
Substitution |
 |
Alternate Interior Angles Theorem |
m m |
Definition of Congruence |
| m1 + m3 + m2 = 180° |
Substitution |
through point Y. Call this line 
