Points of Concurrency - Bisectors, Medians, Altitudes
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 ___.
Angle Bisector
The segment drawn from a vertex that bisects that angle is the ___.
Altitude
The segment that makes a right angle and goes through the vertex is the ___.
Orthocenter
The three altitudes of a triangle intersect at the
Incenter
The three angle bisectors of a triangle intersect at the
Centroid
The three medians of a triangle intersect at the
Circumcenter
The three perpendicular bisectors of a triangle intersect at the
Incenter
The triangle center shown is the ___.
Circumcenter
Which point of concurrency is located on the hypotenuse of a right triangle?
Orthocenter
Which point of concurrency is located on the right angle of a right triangle?
Centroid
Which point of concurrency is shown?
Circumcenter
Which point of concurrency is shown?
Orthocenter
Which point of concurrency is shown?
Incenter
Which point of concurrency is shown?.
Orthocenter and Circumcenter
Which two points of concurrency are always located outside of an obtuse triangle?
never
(Always/sometimes/never?) The incenter is _______ outside the triangle
sometimes
(Always/sometimes/never?) The median of a triangle is _______ the same as the angle bisector
never... (only in an isosceles or equilateral triangle)
(always/sometimes/never?) In a scalene triangle, the angle bisector is also the median
always
(always/sometimes/never?) In an equilateral triangle, the centroid is also the circumcenter.
20
If a median has a length of 30, how long is the segment from vertex to centroid? (the big piece)
12
If the big piece of the median (vertex to centroid) is 24, how long is the small piece (centroid to side)?
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?
Centroid
It divides each median into two sections at a 2:1 ratio.
Incenter
It is equidistant from the three sides of a triangle.
Circumcenter
It is equidistant from the three vertices of a triangle.
