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: m1 + m2 + m3 = 180°
Statements | Reasons |
Construct a line parallel to through point Y. Call this line |
Construction |
m1 + m5 = mAYX | Angle Addition Postulate |
mAYX + m4 = 180° | Linear Pair Postulate |
m1 + m5 + m4 = 180° | Substitution |
Alternate Interior Angles Theorem | |
m2 = m4 m3 = m5 |
Definition of Congruence |
m1 + m3 + m2 = 180° | Substitution |