Geometry
remarkable points and straight lines
A median is a line that connects the vertex of a triangle to the midpoint of the opposite side.
The three medians of a triangle converge at a point called centroid or geometric barycenter or center of mass.
An altitude is a line through a vertex of a triangle and perpendicular to the opposite side.
The three altitudes of a triangle converge at a point called orthocenter.
An angle bisector is a line through a vertex that cuts its angle in half. It is the geometric place of the points which are equidistant to both sides, too.
The three angle bisectors of a triangle converge at a point called incenter, the center of the triangle’s incircle.
A perpendicular bisector is the line that cuts a side in half and it is perpendicular to it. It is the geometric place of the points which are equidistant to both vertices, too.
The three perpendicular bisectors of a triangle converge at a point called circumcenter, the center of the triangle’s circumcircle.
True-False Question
Decide if the following sentences are true or false:
a) The three angle bisectors converge at a point called circumcenter
b) The orthocenter is the center of the incircle
c) The three pependicular bisectors converge at a point called circumcenter
d) The orthocenter can be out of the triangle
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