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Coordinate Proof: Rectangle Diagonals

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About This MicroSim

This interactive visualization demonstrates how to use coordinate geometry to prove that the diagonals of a rectangle are congruent. By adjusting the rectangle dimensions, students can see the proof works for all rectangles.

The Proof Strategy

  1. Smart placement - Put vertex A at the origin (0, 0)
  2. Use variables - Let sides have lengths a and b
  3. Apply distance formula - Calculate both diagonal lengths
  4. Compare results - Show AC = BD = √(a² + b²)

How to Use

  1. Adjust sliders to change rectangle dimensions a and b
  2. Hover over vertices to see their coordinates
  3. Watch formulas update with actual values
  4. Observe that both diagonals always have the same length

Interactive Features

  • Adjustable dimensions - Change a and b with sliders
  • Live calculations - See numeric values update in real-time
  • Hover tooltips - View coordinates at each vertex
  • Color-coded - Diagonals match their formula boxes

Why Coordinate Proofs?

Coordinate proofs combine geometry with algebra:

  • Precise - Uses exact calculations, not measurements
  • Universal - Variables prove it for ALL rectangles
  • Powerful - Leverages algebraic tools

Strategic Placement Tips

  • Place one vertex at the origin (0, 0)
  • Align sides with axes when possible
  • Use variables for general proofs
  • Keep figures in the first quadrant

Learning Objectives

  • Apply the distance formula in proofs
  • Understand strategic placement of figures
  • Connect geometry and algebra
  • Generalize proofs using variables

Bloom's Taxonomy Level

Applying - Using coordinate geometry formulas to prove properties.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/coordinate-proof-diagonals/main.html"
        height="552px"
        width="100%"
        scrolling="no"></iframe>

References

  1. Coordinate Geometry - Math Is Fun
  2. Distance Formula - Khan Academy