Question

what is the first step to construct the centroid of a triangle? a. construct the perpendicular bisectors of each side b. identify the midpoints of each side c. construct the angle bisectors of each angle d. draw a circle in the triangle which point divides the medians into a 2:1 ratio? a. circumcenter b. tangent c. centroid d. incenter which point is equidistant from all vertices of a triangle? a. incenter b. circumcenter c. centroid d. tangent

Explanation:

1. The centroid of a triangle is the point of intersection of its medians. To construct the medians, we first need to identify the mid - points of each side of the triangle.
2. The centroid of a triangle divides each median in a 2:1 ratio, with the longer segment towards the vertex.
3. The circumcenter of a triangle is the point that is equidistant from all the vertices of the triangle. It is the center of the circum - circle.

Answer:

1. B. Identify the midpoints of each side
2. C. Centroid
3. B. Circumcenter