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Triangle Inequalities

The triangle inequality theorem states that in any triangle, the sum of the lengths of any two sides is greater than the length of the thirds side.

So, for any triangle:

Triangle Notation

AB+BC>AC

AC+BC>AB

AC+AB>BC

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Now that we've explained the basic concept of triangle inequalities in geometry, let's scroll down to work on specific geometry problems relating to this topic.

Reverse Triangle Inequality

Reverse Triangle Inequality Theorem

Hinge open to 2 different angles

Hinge Theorem

Scalene Triangle

Converse of the Scalene Triangle Inequality

Scalene triangle

The Scalene Inequality Theorem

Triangle inequality theorem - A to B is shortest

Triangle Inequality Theorem

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Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

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