Question

the segment that extends from the vertex of a triangle to the ____ side and is perpendicular to the side of the triangle is called the altitude.
options: opposite, centroid, circumcenter, midpoint

1. choose the correct answer.

the ____ is the point of intersection of the medians of a triangle.
options: opposite, vertex, centroid, circumcenter

Explanation:

First Question (About Altitude)

To determine the correct term for the blank in the altitude definition: Recall the definition of an altitude of a triangle. An altitude is a segment from a vertex to the opposite side (or its extension) that is perpendicular to that side. "Centroid" is the intersection of medians, "circumcenter" is the intersection of perpendicular bisectors, and "midpoint" is the middle of a segment. So the correct term is "opposite".

To find the term for the intersection of medians: Recall triangle terminology. The centroid is defined as the point where the three medians of a triangle intersect. "Opposite" refers to a side relative to a vertex, "vertex" is a corner of the triangle, and "circumcenter" is for perpendicular bisectors. So the correct term is "centroid".

Answer:

A. opposite (assuming the first option is labeled A, but since options are given as radio buttons with "opposite" as first, the answer is the option with "opposite")

Second Question (About Medians' Intersection)