Question

question 7 of 10
many of the same constructions the greeks performed only with a straightedge and compass can be done using only a straightedge and tracing paper.

a. true
b. false

Explanation:

Analyze the geometric tools and construction capabilities

The statement compares classical Greek constructions (using only an unmarked straightedge and a compass) with constructions performed using only a straightedge and tracing paper (which allows for folding, reflecting, and copying angles/segments).

Compare construction systems

Tracing paper allows for paper folding (origami) geometry. Folding paper can easily construct perpendicular bisectors, angle bisectors, parallel lines, and copy line segments or angles. In fact, paper folding (which can be done with tracing paper and a straightedge) can perform all constructions possible with a compass and straightedge, and can even solve classical problems that are impossible with a compass and straightedge alone (such as trisecting an angle or doubling a cube). Therefore, many of the same constructions can indeed be done using this alternative set of tools.

Determine the truth value

Since paper folding with a straightedge is mathematically more powerful than or equivalent to classical compass-and-straightedge constructions for these tasks, the statement is true.

Answer:

• A. True (Correct answer)
• B. False