Points of Concurrency

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides equal in length and the included angle of one triangle is larger than the included angle of the other, then the third side of the triangle with the larger angle is longer.

Front

What is a point of concurrency?

Back

A point of concurrency is a point where three or more lines intersect. In triangles, common points of concurrency include the centroid, circumcenter, incenter, and orthocenter.

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. It is equidistant from all three vertices of the triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is the center of mass of the triangle and divides each median into a 2:1 ratio.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 5 and 15, what is the range for the length of the third side?

Back

10 < x < 20, where x is the length of the third side.

Front

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

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is the relationship between the angles and sides in a triangle according to the Hinge Theorem?

Back

In a triangle, if one angle is larger than another, the side opposite the larger angle is longer than the side opposite the smaller angle.