Medians and Altitudes of Triangles

Front

What is a median in a triangle?

Back

A median is a segment whose endpoints are a vertex of the triangle and 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

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, located 2/3 of the distance from each vertex to the midpoint of the opposite side.

Front

How do you find the length of a segment from a vertex to the centroid?

Back

The length from a vertex to the centroid is 2/3 the length of the median from that vertex.

Front

What is the relationship between medians and centroids?

Back

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

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.

Front

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

Back

BG = 12.

Front

What is the formula to find the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * √(2a² + 2b² - c²), 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 a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle.

Front

What is the orthocenter of a triangle?

Back

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