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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

AB is an altitude.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.C.A.3