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.