Question

Which of these needs to be completed first in order to construct a circle that circumscribes a triangle?

A. the perpendicular bisectors of any two sides of the triangle

B. the lines perpendicular to any two sides of the triangle

C. the altitudes of any two sides of the triangle

D. the medians of any two sides of the triangle

Answer 1

The perpendicular bisectors of any two sides of the triangle need to be completed first to construct a circle that circumscribes a triangle.

Step-by-step explanation:

In order to construct a circle that circumscribes a triangle, the perpendicular bisectors of any two sides of the triangle need to be completed first.

A perpendicular bisector is a line that passes through the midpoints of a side of a triangle and is perpendicular to that side. When the perpendicular bisectors of any two sides of a triangle are drawn, they intersect at a single point, which is the center of the circumcircle. The radius of the circumcircle is then the distance from the center to any vertex of the triangle.

Therefore, option A is the correct answer.