Geometry 5.1-5.4

15 terms by addieg21 

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Centroid

the point of concurrency of the medians of a triangle.

Centroid requires

midpoint, opposite vertex

Circumcenter

the point of concurrency for perpendicular bisectors

Circumcenter requires

perpendicular slope, midpoint

Incenter

the point of concurrency for angle bisectors

Median of a triangle

A segment whose endpoints are the midpoint of one side of a triangle and the opposite vertex.

A segment whose endpoints are the midpoint of one side of a triangle and the opposite vertex.
Orthocenter is the point of concurrency for

altitudes

Where is the centroid in a triangle?

Inside

Where is the orthocenter of a right triangle?

On the vertex of right angle

Where is the orthocenter of an acute triangle?

Inside

Where is the orthocenter of an obtuse triangle?

Outside

Where must the centroid always be located regardless of acute, right or obtuse?

Inside the triangle

For every type of triangle (scalene, obtuse, acute, right, etc...) the three medians in a triangle will

intersect at exactly 1 point

When the triangle is acute

then the orthocenter falls inside the triangle.

When the triangle is obtuse

the orthocenter falls outside the triangle

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