Medians and Altitudes of Triangles

Front

What is a median of a triangle?

Back

A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

Front

What is an altitude of a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

The centroid of a triangle is the point where the three medians are concurrent.

Front

What is the orthocenter of a triangle?

Back

The orthocenter of a triangle is the point where the three altitudes are concurrent.

Front

What does the Centroid Theorem state?

Back

The Centroid Theorem states that the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.

Front

If RS = 21, what is the length of SV according to the Centroid Theorem?

Back

7

Front

What is the relationship between medians and centroids in 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 many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the significance of the orthocenter in a triangle?

Back

The orthocenter is significant as it helps in understanding the triangle's altitudes and their concurrency.

Front

Can the orthocenter be outside the triangle?

Back

Yes, the orthocenter can be outside the triangle in obtuse triangles.