Final answer:
The ancient Greeks used a straightedge and compass in their constructions to create precise geometric constructions.
Step-by-step explanation:
The ancient Greeks used only a straightedge and compass in their constructions because these tools allowed them to create geometric constructions that were accurate and precise. The straightedge was used to create straight lines, while the compass was used to create circles and arcs. These basic tools were essential in Greek mathematics and geometry, as they enabled the Greeks to explore and prove geometric theorems.
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