Medians and Centroid and Altitudes and Orthocenter

Front

What is the point of concurrency of the three altitudes of a triangle?

Back

Orthocenter

Front

What is the median of a triangle?

Back

A line segment joining a vertex to the midpoint of the opposite side.

Front

In triangle ΔXYZ, if YB, XC, and ZA are medians, what is the relationship between the segments?

Back

Each median divides the triangle into two smaller triangles of equal area.

Front

What is the point of concurrency of the three medians of a triangle called?

Back

Centroid

Front

What is the circumcenter of a triangle?

Back

The point where the three perpendicular bisectors of the sides intersect.

Front

If YC = 10 in triangle ΔXYZ, what is the length of ZC if YB, XC, and ZA are medians?

Back

ZC = 10.

Front

What is the altitude of a triangle?

Back

A perpendicular segment from a vertex to the line containing the opposite side.

Front

In triangle ΔXYZ, if YC = 15, what is the length of YZ if YB, XC, and ZA are medians?

Back

YZ = 30.

Front

What is the incenter of a triangle?

Back

The point where the three angle bisectors of a triangle intersect.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices.