Special segments in triangles

Front

What is the definition of a centroid in 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

If G is the centroid of triangle ABC, what is the relationship between the segments AG, GB, and GC?

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 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 relationship between a midsegment and the sides of the triangle?

Back

A midsegment is parallel to the third side of the triangle and its length is half the length of that side.

Front

How do you find the coordinates of the centroid G of triangle ABC with vertices A(x1, y1), B(x2, y2), C(x3, y3)?

Back

The coordinates of the centroid G are given by G = (\frac{x1 + x2 + x3}{3}, \frac{y1 + y2 + y3}{3}).

Front

What type of segments are drawn from the centroid of a triangle?

Back

Medians are drawn from the centroid to the vertices of the triangle.

Front

If QR is a midsegment of triangle BCD, what can be said about the lengths of segments BD and CD?

Back

BD and CD are each twice the length of QR.

Front

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

Back

Front

What is the significance of the centroid in terms of triangle balance?

Back

The centroid is the point at which a triangle can be balanced on the tip of a pencil, as it represents the center of mass.