Concurrent Lines in a Triangle

Front

What is the point of concurrency where the angle bisectors of a triangle intersect?

Back

Incenter

Front

If BZ is a median in triangle ABC, and AZ = 2x + 5, CZ = 6x - 3, BZ = x + 5, find CZ when x = 2.

Back

CZ = 9

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of the triangle intersect.

Front

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

Back

GC = 8

Front

What is the point of concurrency where the altitudes of a triangle intersect?

Back

Orthocenter

Front

If S is the incenter of triangle ABC, what type of segments are drawn from S?

Back

Angle bisectors

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.

Front

If the lengths of the sides of triangle ABC are 3, 4, and 5, what type of triangle is it?

Back

Right triangle.

Front

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

Back

The centroid divides each median into a ratio of 2:1.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is the center of the circle inscribed in the triangle.