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

What is the circumcenter of a triangle?

Back

The circumcenter is the point of concurrency of the three perpendicular bisectors of a triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point of concurrency of the three angle bisectors of a triangle.

Front

What is the relationship between the centroid and the medians?

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

How do you 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

What is the point of concurrency?

Back

A point of concurrency is a point where three or more lines intersect.

Front

What are perpendicular bisectors?

Back

Perpendicular bisectors are lines that divide a segment into two equal parts at a right angle.

Front

What is the significance of the circumcenter?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it the center of the circumcircle.

Front

What is the significance of the incenter?

Back

The incenter is equidistant from all three sides of the triangle, making it the center of the incircle.