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Hinge Theorem Visualization

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About This MicroSim

This visualization demonstrates the Hinge Theorem using a door hinge analogy. Adjust the angle slider to see how changing the included angle affects the length of the opposite side.

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first is larger, then the third side of the first triangle is longer.

Door Hinge Analogy

Think of a door hinge: - The two door/frame pieces are like the two equal sides - The hinge opening angle is like the included angle - The gap between endpoints is like the third side

Wider hinge opening = Greater distance between endpoints

How to Use

  1. Observe the left triangle (fixed at 40°)
  2. Adjust the slider to change the right triangle's included angle
  3. Compare the third sides (shown in red)

Key Observations

  • When both angles are equal, the third sides are equal
  • Larger included angle → Longer opposite side
  • Smaller included angle → Shorter opposite side

Learning Objectives

  • Understand the relationship between angle size and opposite side
  • Apply the Hinge Theorem to compare triangles
  • Analyze how changing angles affects side lengths

Bloom's Taxonomy Level

Understanding, Applying, and Analyzing

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/hinge-theorem/main.html"
        height="502px"
        width="100%"
        scrolling="no"></iframe>