Geometry: Points of Concurrency
Median
The line segment joining a vertex to the midpoint of the opposite side is the ___.
Perpendicular bisector
The line segment that is both perpendicular to a side of a triangle and passes through its midpoint is the ___.
Midsegment
The pictures shows what kind of segment in a triangle?
Centroid
The point of concurrency in which the medians are 2/3 the distance from each vertex to the midpt of the opposite side
Centroid
The point of concurrency shown is the ___.
Circumcenter
The point of concurrency shown is the ___.
Incenter
The point of concurrency shown is the ___.
Orthocenter
The point of concurrency shown is the ___.
Incenter
The point of concurrency that is equidistant from the three sides of a triangle.
Circumcenter
The point of concurrency that is equidistant from the three vertices of a triangle.
Centroid
The point of concurrency that is the center of gravity or balancing point of a triangle.
Angle Bisector
The segment drawn from a vertex that bisects that angle is the ___.
Orthocenter
Three altitudes of a triangle intersect at the
Incenter
Three angle bisectors of a triangle intersect at the
Centroid
Three medians of a triangle intersect at the
Circumcenter
Three perpendicular bisectors of a triangle intersect at the
Nine-Point Circle
What is created by the arcs connecting a triangle's three midpoints, each foot of the altitudes, and the midpoints from each vertex to the orthocenter?
2:1 ratio
What is the ratio of the radius of the circumcircle to the radius of the Nine-Point Circle?
vertices
A circumcenter is equidistant from the _____ of a triangle
Midsegment
A segment that goes from a midpoint of one side of a triangle to the midpoint of another side of a triangle.
Midsegment
A segment that is parallel to the side of a triangle and half as long.
sides
An incenter is equidistant from the ____ of a triangle
Euler Line
For any triangle the orthocenter, centroid and circumcenter will lie on this line
Altitude
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Angle Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Median
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Perpendicular Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
Altitude
The "height" of a triangle is the ___.