Points of Concurrency Practice

Front

What is the definition of an orthocenter of a triangle?

Back

The point where the altitudes of the triangle intersect.

Front

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

Back

8

Front

Find the length of PO.

Back

32

Front

What is the definition of an altitude of a triangle?

Back

A line segment drawn from a vertex perpendicular to the opposite side or to the line containing the opposite side.

Front

What is the definition of a median of a triangle?

Back

A line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is the definition of a centroid in a triangle?

Back

The point where the three medians of the triangle intersect.

Front

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

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

What is the definition of a circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides of the triangle intersect.

Front

What is the definition of an incenter of a triangle?

Back

The point where the angle bisectors of the triangle intersect.

Front

How do you find the length of a median in a triangle?

Back

Use the formula: Median = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.