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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