The statement given is: "Given only a compass and straightedge, Greeks were able to construct any geometric object they wished."
The correct answer is:
B. False
Explanation:
1. The statement refers to the ancient Greek mathematical concept of geometric constructions using only a compass and straightedge.
2. While the Greeks were able to construct basic geometric shapes like triangles, squares, and circles using only a compass and straightedge, there were limitations to what could be constructed.
3. Not all geometric objects can be constructed using only a compass and straightedge. For example, it is impossible to trisect an angle into three equal parts using only these tools, as proven by the ancient Greeks and later by modern mathematics.
4. Therefore, the statement that Greeks could construct any geometric object they wished with only a compass and straightedge is false due to the limitations of these tools in certain constructions.
