Question

question 9 of 25
which of these tools or constructions is needed to construct an equilateral triangle?
a. parallel line through a point
b. compass
c. perpendicular bisector
d. angle bisector

Explanation:

Step1: Recall construction of equilateral triangle

To construct an equilateral triangle, we start with a side length. Using a compass, we can draw arcs of the same radius (equal to the side length) from the endpoints of the initial side. The intersection of these arcs gives the third vertex.

Step2: Analyze other options

• A parallel line through a point is not used in the basic construction of an equilateral triangle.
• A perpendicular bisector is used for different constructions (e.g., constructing a perpendicular to a line segment), not for the core steps of an equilateral triangle construction.
• An angle bisector is also for different geometric tasks (like bisecting an angle), not essential for constructing an equilateral triangle from scratch.

So, the compass is needed for the construction of an equilateral triangle.

Answer:

B. compass