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Triangle Inequality Explorer

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About This MicroSim

This interactive tool demonstrates the Triangle Inequality Theorem by allowing you to test different combinations of side lengths and see whether they can form a valid triangle.

How to Use

  1. Adjust the sliders to set the lengths of sides a, b, and c
  2. Watch the construction attempt to form a triangle
  3. Check the inequalities displayed in the top left
  4. See the result at the bottom showing whether a triangle can form

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

All three conditions must be satisfied: - a + b > c - b + c > a - a + c > b

Visual Feedback

Valid Triangle (Green)

  • Arcs intersect at point C
  • Complete triangle is drawn
  • All three inequalities show ✓

Invalid Triangle (Red)

  • Arcs do not intersect
  • Gap shown between arcs
  • Failed inequality shows ✗

Key Insights

  • The longest side determines the "critical" inequality
  • If the two shorter sides don't sum to more than the longest, no triangle forms
  • When a + b = c exactly, you get a straight line (degenerate case)

Learning Objectives

  • Understand the Triangle Inequality Theorem
  • Apply the theorem to determine valid triangles
  • Evaluate which side length combinations work

Bloom's Taxonomy Level

Understanding, Applying, and Evaluating

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/triangle-inequality-explorer/main.html"
        height="602px"
        width="100%"
        scrolling="no"></iframe>