Points of Concurrency Check

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

When is the circumcenter of a triangle located inside the triangle?

Back

The circumcenter is located inside the triangle when the triangle is acute.

Front

What is the relationship between the segments AG and GE if AG is twice as long as GE?

Back

If AG is twice as long as GE, then if GE = x, then AG = 2x.

Front

What does it mean for an altitude to be perpendicular to a side of a triangle?

Back

An altitude is a line segment from a vertex to the opposite side that forms a right angle (90 degrees) with that side.

Front

What is a median in a triangle?

Back

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

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 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 incircle.

Front

How can you determine the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection is the circumcenter.

Front

What is the significance of the midpoints in a triangle?

Back

Midpoints are used to define medians and can help in constructing the centroid and other points of concurrency.

Front

What is the difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.