7-5 Centroid Practice

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

If the length of a median is known, how can you find the lengths of the segments it creates?

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.

Front

If G is the centroid of triangle ABC and BE = 18, what is the length of BG?

Back

BG = 12, since the centroid divides the median in a 2:1 ratio.

Front

If DL = 24, what is DG?

Back

DG = 8, based on the relationship of segments in the triangle.

Front

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

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

If ZO = 24 and SZ = 3a - 9, how do you find the value of a?

Back

Set up the equation 3a - 9 = 24, solve for a to get a = 11.

Front

What is the formula to find 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, b, and c are the lengths of the sides of the triangle.

Front

If CF, BE, and AD are the medians of a triangle and BF = 10, what is AF?

Back

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

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 is used in various applications in geometry and physics.