Points of Concurrency

Front

What is a point of concurrency?

Back

A point where three or more lines intersect in a triangle.

Front

What are the three main points of concurrency in a triangle?

Back

Centroid, Incenter, and Circumcenter.

Front

What is the Centroid of a triangle?

Back

The point where the three medians intersect; it is the center of mass.

Front

What is the Incenter of a triangle?

Back

The point where the three angle bisectors intersect; it is equidistant from all sides.

Front

What is the Circumcenter of a triangle?

Back

The point where the three perpendicular bisectors intersect; it is equidistant from all vertices.

Front

What is the Orthocenter of a triangle?

Back

The point where the three altitudes intersect.

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

How do you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: a + b > c, a + c > b, b + c > a.

Front

What is the formula for finding the range of the third side of a triangle given two sides?

Back

If the sides are a and b, then the third side x must satisfy: |a - b| < x < a + b.

Front

What is the significance of the Incenter in a triangle?

Back

It is the center of the inscribed circle (incircle) that touches all sides.