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Triangles - Part I

The content provides an in-depth exploration of fundamental properties and rules governing the geometry of triangles, essential for GRE exam preparation.
  • The sum of the three angles inside any triangle is exactly 180 degrees, a foundational geometric principle.
  • Triangles cannot have more than one right or obtuse angle, ensuring at least two angles are acute.
  • The largest angle in a triangle is always opposite the longest side, and the smallest angle is opposite the shortest side.
  • The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side.
  • For any two sides of a triangle, the length of the third side must be greater than the difference and less than the sum of these two sides.
Fundamental Properties of Triangles
Angles and Their Sum in Triangles
Triangle Inequality Theorem
Determining the Lengths of Triangle Sides