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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 .
Given:
Prove:
Statements | Reasons |
Construct a line parallel to through point . Call this line |
Construction |
Angle Addition Postulate | |
Linear Pair Postulate | |
Substitution | |
Alternate Interior Angles Theorem | |
Definition of Congruence | |
Substitution |