Centers of Triangles

The centroid is always inside the triangle.

True

The incenter must always be inside the triangle

True

The altitude of a triangle is the same as its perpendicular bisector.

False

The circumcenter is located outside of the triangle when the triangle is acute.

False

The incenter is located outside the triangle when the triangle is obtuse.

False

The incenter, circumcenter and orthocenter will always fall in a straight line.

False

The measure from a vertex to the centroid is always half the measure from the centroid to midpoint on the side opposite the vertex.

False

In order for all four centers to be outside the triangle, the triangle must be....

It can't ever happen.

If a triangle is a right triangle, then the circumcenter will be located on the hypotenuse.

True

If the triangle is a right triangle, then the orthocenter will be on the vertex of the right angle.

True

If the triangle is equilateral then the centroid, orthocenter, circumcenter and incenter will be at the same point.

True

If the triangle is obtuse then the orthocenter and circumcenter will be outside the triangle.

True

The median is a segment that connects...

a vertex to the middle of another vertex.

The intersection of the medians of a triangle is called

centroid

This center will balance a triangle.

centroid

There is always a 2:1 ratio between the distance from the orthocenter to the centroid and the.

centroid to the circumcenter

The intersection of the perpendicular bisectors of a triangle is called......

circumcenter

The intersection of the angle bisectors of a triangle is called.....

incenter

The intersection of the altitudes of a triangle is called.....

orthocenter

When a triangle is a right triangle, then.

the altitude will also be one of the legs of the triangle.