Centroid and Centers of Triangles Flashcard

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 AC = 16, what is AM?

Back

AM = 8 (since the centroid divides each median in a 2:1 ratio).

Front

If CF, BE, and AD are the medians of the triangle and BF = 10, find AF.

Back

AF = 10 (the centroid divides the median into two segments with a 2:1 ratio).

Front

What is the relationship between the centroid and the medians of a triangle?

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

If LB = 4, what is CL?

Back

CL = 4 (the centroid divides the median into two equal parts).

Front

What type of segments are drawn to find the centroid of a triangle?

Back

Medians are drawn to find the centroid of a triangle.

Front

What is the formula for finding the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

Centroid (G) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: Median = √(2a² + 2b² - c²)/4, where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.

Front

What is the significance of the centroid in real-world applications?

Back

The centroid is used in various fields such as engineering, architecture, and physics to determine the center of mass and balance of structures.