Question

question 8 of 10

which of the following are techniques used in geometric constructions with paper folding?

check all that apply.

a. creating arcs and circles with the compass
b. folding the paper and aligning marks seen through the paper
c. measuring line segments by folding the paper and matching the endpoints
d. marking points

Explanation:

Identify paper folding techniques

Using the Paper Folding Constructions knowledge point, we analyze each option to determine if it is a valid technique used in geometric constructions with paper folding:

• Option A: "Creating arcs and circles with the compass" is a technique of classical compass-and-straightedge construction, not paper folding.
• Option B: "Folding the paper and aligning marks seen through the paper" is a fundamental technique of paper folding (origami geometry) used to construct perpendicular bisectors, angle bisectors, and other geometric relationships.
• Option C: "Measuring line segments by folding the paper and matching the endpoints" is a standard method in paper folding to compare lengths or copy segments without a ruler.
• Option D: "Marking points" is a necessary step in any geometric construction, including paper folding, to define vertices, intersections, or endpoints.

Therefore, options B, C, and D are techniques used in paper folding constructions.

Answer:

• (A) Creating arcs and circles with the compass
• (B) Folding the paper and aligning marks seen through the paper (Correct answer)
• (C) Measuring line segments by folding the paper and matching the endpoints (Correct answer)
• (D) Marking points (Correct answer)