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What makes a triangle equilateral, isosceles, or scalene?

How are these triangles the same? How are they different? Manipulate the triangles by dragging their blue corner points. What happens to their side lengths?

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closest unit squares relative to their inclination
Long Division with Feedback (v4)
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Constructions
Pythagoras or Pythagorean Theorem
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Differential Calculus
Angles