Flashcard 2-5 all Centers of Triangles

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the Circumcenter of a triangle?

Back

The Circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle, which passes through all three vertices.

Front

What is the Centroid of a triangle?

Back

The Centroid is the point where the three medians of a triangle intersect. It is the center of mass and divides each median into a 2:1 ratio.

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

How do you find the length of a segment in a triangle given the centroid?

Back

The length of a segment from a vertex to the centroid is two-thirds the length of the median from that vertex.

Front

If AB = 18 and X is the centroid, what is AW?

Back

AW = 9 (since the centroid divides the median in a 2:1 ratio).

Front

What is the relationship between the circumcenter and the circumradius?

Back

The circumradius is the radius of the circumcircle, which is centered at the circumcenter and passes through all three vertices of the triangle.

Front

How do you find the distance from the incenter to a side of the triangle?

Back

The distance from the incenter to a side of the triangle is the radius of the incircle, which is tangent to all three sides.

Front

If G is the circumcenter, how do you find the length of AD?

Back

Use the properties of the circumcircle and the triangle's dimensions to calculate AD.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is the balance point of the triangle and is always located inside the triangle.