Points of Concurrency in Triangles

Front

What is the point of concurrency that is the intersection of the angle bisectors of a triangle?

Back

Incenter

Front

What is the point of concurrency that is the intersection of the altitudes of a triangle?

Back

Orthocenter

Front

If G is the centroid of triangle ABC and GF= 4, what is the length of GC?

Back

8

Front

If X is the centroid of the triangle and AZ = 24, what is AX?

Back

16

Front

What is the point of concurrency that is the intersection of the perpendicular bisectors of the sides of a triangle?

Back

Circumcenter

Front

Define centroid in the context of triangles.

Back

The centroid is the point of concurrency of the medians of a triangle, and it divides each median into a ratio of 2:1.

Front

What is the relationship between the centroid and the triangle's vertices?

Back

The centroid is located 2/3 of the distance from each vertex along the median.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is equidistant from all sides of the triangle and is the center of the inscribed circle.

Front

How do you find the circumcenter of a triangle?

Back

The circumcenter can be found by constructing the perpendicular bisectors of the sides of the triangle.

Front

What is the relationship between the orthocenter and the triangle's altitudes?

Back

The orthocenter is the point where all three altitudes of a triangle intersect.