Question

given only a compass and straightedge, greeks were able to construct only regular polygons and circles, thus leaving many constructions impossible to complete.

a. true
b. false

Explanation:

Analyze the historical statement

Using the Greek Geometry History and Compass and Straightedge Construction knowledge points

The statement claims that the Greeks were able to construct "only regular polygons and circles" using a compass and straightedge. This is historically inaccurate. With these tools, they could construct many other geometric figures, such as non-regular polygons, parallel and perpendicular lines, angle bisectors, and specific segments of arbitrary lengths.

Evaluate the impossibility claim

Using the Impossible Problems knowledge point

While it is true that certain classic problems are impossible to solve using only a compass and straightedge (such as squaring the circle, doubling the cube, and trisecting an arbitrary angle), the premise that they could only construct regular polygons and circles is false. Therefore, the overall statement is false.

Answer:

• A. True
• B. False (Correct answer)