FHS - Medians & Altitudes of Triangles

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of the triangle intersect. It is also the center of mass of the triangle.

Front

If AZ = 24 and X is the centroid, what is the length of AX?

Back

AX is 16. The centroid divides each median into a ratio of 2:1.

Front

What are the special segments that intersect at the circumcenter of a triangle?

Back

The circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

Is segment AB a median, altitude, neither, or both if it connects a vertex to the midpoint of the opposite side?

Back

AB is a median.

Front

Is segment AB a median, altitude, neither, or both if it is perpendicular to the opposite side?

Back

AB is an altitude.

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle and is the center of the circumcircle.