Centroid, Midsegment, Median

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 is a median in a triangle?

Back

A median is a line segment that connects 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 divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

If a median is divided by the centroid, what is the ratio of the segments?

Back

The ratio is 2:1, with the longer segment being from the vertex to the centroid.

Front

What is a midsegment in a triangle?

Back

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

Front

What is the length of a midsegment in relation to the sides of the triangle?

Back

The length of a midsegment is half the length of the third side of the triangle.

Front

If BF = 10 in triangle ABC, what is AF if CF is a median?

Back

AF = 10, since the median divides the opposite side into two equal segments.

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 the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle, where it would balance perfectly if made of a uniform material.