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Answers will vary. One of the advantages is the precision with which we can construct figures. Another one is that the measurement tools combined with the ability to modify figures dynamically allow us to observe changes and make conjectures about what aspects of the figures are invariant. Most importantly, you can test several hundred cases with just one construction. For example, if you want to know something about right triangles, you could draw numerous cases, or you could construct just one and change it into all those cases you drew (and more). When we construct something, we know the results are true for all cases. Nevertheless, these would still be conjectures, and conjectures must be proved.
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