CH 5 Which Points of Concurrency in Triangles?

Front

What is the point of concurrency where the three medians of a triangle intersect?

Back

Centroid

Front

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

Back

Circumcenter

Front

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

Back

Incenter

Front

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

Back

Orthocenter

Front

Define the Centroid of a triangle.

Back

The Centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

Define the Circumcenter of a triangle.

Back

The Circumcenter is the point where the three perpendicular bisectors of a triangle intersect, and it is equidistant from all three vertices.

Front

Define the Incenter of a triangle.

Back

The Incenter is the point where the three angle bisectors of a triangle intersect, and it is equidistant from all three sides.

Front

Define 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 Centroid and the vertices of a triangle?

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

How can you find the Circumcenter of a triangle using its vertices?

Back

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