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Circumcenter, Orthocenter, Incenter, Centroid EOC Review
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Terms in this set (35)
The medians of a triangle are __________
concurrent
The ________ of a triangle are concurrent.
medians
The medians of a ___________ are concurrent
triangle
The point of concurrency, called the _______, cuts the median into two segments that have lengths with a fixed 2:1 ratio.
centroid
The point of concurrency, called the centroid, does what?
Cuts the median into two segments that have lengths with a fixed 2:1 ratio.
The centroid is ______from the vertex.
2/3 away
The centroid is ______from the midpoint.
1/3 away
The _______ is 2/3 from the vertex, 1/3 from the midpoint.
Centroid
Median of a triangle
A segment whose endpoints are the midpoint of one side of a triangle and the opposite vertex.
Centroid
the point of concurrency of the medians of a triangle.
How many medians are in each triangle?
3- one median to correspond to each side.
For every type of triangle (scalene, obtuse, acute, right, etc...) the three medians in a triangle will
intersect at exactly 1 point
The medians of a triangle are:
concurrent.
The point of concurrency of the medians of a trianlge
Centroid
Unlike the circumcenter and the incenter, the centroid is______________
NOT the center of a mysterious circle.
With a median, you don't have to have ____________
perpendicularity
Instead of perpendicularity in a median, you have __________
two endpoints
Where must the centroid always be located regardless of acute, right or obtuse?
Inside the triangle
What kind of triangle would have perpendicularity with the medians?
Equilateral
The centroid is the first and only ____________
point of concurrency for triangles that fixes a ratio of lengths.
The ________ is the first and only point of concurrency for triangles that fixes a ratio of lengths.
Centroid
Circumcenter is the point of concurrency for
perpendicular bisectors
Incenter is the point of concurrency for
angle bisectors
Orthocenter is the point of concurrency for
altitudes
Centroid is point of concurrency for
medians
Circumcenter requires
perpendicular slope, midpoint
Orthocenter requires
perpendicular slope, opposite vertex
Centroid requires
midpoint, opposite vertex
Where is the circumcenter in a right triangle?
Midpoint of hypotenuse
Where is the incenter in a triangle?
Inside
Where is the orthocenter of an acute triangle?
Inside
Where is the orthocenter of a right triangle?
On the vertex of right angle
Where is the orthocenter of an obtuse triangle?
Outside
Where is the centroid in a triangle?
Inside
Concurrency deals with
coplanar lines intersecting at exactly one point.
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