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

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle and is parallel to the third side.

Front

How does the length of a midsegment compare to the length of the side it is parallel to?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

What is the relationship between the centroid and the lengths of the segments it creates?

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 triangle has a median of length 12, what is the length of the segment from the centroid to the vertex?

Back

The length of the segment from the centroid to the vertex is 8.

Front

What is the altitude of a triangle?

Back

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

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.

Front

If segment EF is parallel to segment GH, what can be said about the lengths of these segments?

Back

If EF is parallel to GH and they are midsegments, then EF is half the length of GH.

Front

What is the formula for finding the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.