Altitudes, Medians, & Centers

Front

In an acute triangle, where is the orthocenter located?

Back

Inside the triangle.

Front

What fraction of the length of a median is the shorter segment created by the centroid?

Back

One third.

Front

What is the center that is the intersection of all altitudes in a triangle?

Back

Orthocenter.

Front

If G is the centroid of triangle ABC and BE= 18, what is the length of BG?

Back

12.

Front

If point H is the centroid of the triangle, what is the length of \overline{EH} if it is given as 18?

Back

18.

Front

What is the definition of a median in a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

The centroid is the point where all three medians intersect, and it divides each median into a ratio of 2:1.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

Front

How many altitudes can be drawn in a triangle?

Back

Three, one from each vertex.