Median & Centroid

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the relationship between the centroid and the medians?

Back

The centroid is the point of concurrency of the three medians of a triangle.

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What type of segments are drawn to find the centroid?

Back

Medians are drawn to find the centroid of a triangle.

Front

What is the formula to find the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

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 difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side.

Front

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

Back

The point of concurrency of the altitudes is called the orthocenter.