Triangles - Relationships & Points of Concurrency

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 is the relationship between the centroid and the segments it creates?

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

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 equidistant from all three vertices of the triangle.

Front

How do you find the length of a segment from the centroid to a vertex?

Back

If the length of the median is known, the length from the centroid to the vertex is 2/3 of the median's length.

Front

What is the orthocenter of a triangle?

Back

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

Front

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

Back

The orthocenter's position (inside, on, or outside the triangle) depends on the type of triangle: acute, right, or obtuse.

Front

If m∠CAP = 34°, what is m∠CAB in triangle ABC?

Back

m∠CAB = 68°.

Front

If G is the centroid of triangle ABC and BE = 18, what is the length of BG?

Back

BG = 12.

Front

If CW = 30 and X is the centroid, what is CX?

Back

CX = 20.

Front

What is the relationship between the circumcenter and the circumradius?

Back

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