#6.3 Medians and Centroids of Triangles

Front

What is the centroid of a triangle?

Back

The centroid of a triangle is the point where the three medians intersect, and it is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

Front

What is a median in the context of triangles?

Back

A median is a segment from a vertex of a triangle to the midpoint of the opposite side.

Front

How do you find the length of a segment from a vertex to the midpoint of the opposite side?

Back

To find the length of the segment (median), you can use the properties of the triangle and the lengths of the sides.

Front

If BL = 12, what is the length of BP if P is the midpoint of segment BL?

Back

BP = 8.

Front

If AL = 27, what is the length of AP if P is the midpoint of segment AL?

Back

AP = 18.

Front

What is the relationship between the lengths of the segments created by the centroid on 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

What is the point of concurrency for the medians of a triangle called?

Back

The point of concurrency for the medians of a triangle is called the centroid.

Front

How many medians can be drawn in a triangle?

Back

Three medians can be drawn in a triangle, one from each vertex to the midpoint of the opposite side.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is significant because it is the balance point of the triangle and divides each median into a 2:1 ratio.

Front

Can the centroid of a triangle lie outside the triangle?

Back

No, the centroid of a triangle always lies inside the triangle.