Unit 2 Points of Concurrency, Use it!

Front

What is the centroid of a triangle?

Back

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

Front

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

Back

If a segment is divided by the centroid in a 2:1 ratio, you can set up an equation based on the lengths of the segments to find the unknown length.

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, and it is equidistant from all three vertices.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's inscribed circle.

Front

What is the orthocenter of a triangle?

Back

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

Front

If FY = x + 6 and YG = 16, what is the value of x if Y is the centroid?

Back

x = 2.

Front

What is the ratio in which the centroid divides each median?

Back

The centroid divides each median in a 2:1 ratio.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.

Front

How can you identify the incenter of a triangle?

Back

The incenter can be identified as the point where the angle bisectors of the triangle meet.

Front

What is the significance of the orthocenter in a triangle?

Back

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