Geometry 6.1-6.3 Quiz

Circumcenter Theorem

The circumcenter of a triangle is equidistant from the vertices of the triangle - If PD, PE, and PF are perpendicular bisectors, then PA = PB = PC

Incenter Theorem

The incenter of a triangle is equidistant from the sides of the triangle. - If AP, BP, and CP are angle bisectors of ABC, then PD = PE = PF

Orthocenter

The lines containing the altitudes of a triangle are concurrent. This point of concurrency is the orthocenter of the triangle. - the vertices of a triangle are each on a line perpendicular to the opposite side of the triangle

Converse of the Angle Bisector Theorem

If a point is in the interior of an angle and is equidistant from the two sides of the angle, then it lies on the bisector of the angle. - the point that lies on the bisector must be located on two segments that are perpendicular to the sides of the angle

Angle Bisector Theorem

If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle. - the point that lies on the bisector must be located on two segments that are perpendicular to the sides of the angle

Converse of the Perpendicular Bisector Theorem

In a plane, if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Perpendicular Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

Centroid Theorem

The centroid of a triangle is 2/3 of the distance form each vertex to the midpoint of the opposite side - AP = 2/3AE, BP = 2/3BF, and CP = 2/3CD

equidistant

equal distance

Point of concurrency

the point of intersection of concurrent lines point of concurrencies: - perpendicular bisector = circumcenter - angle bisector = incenter - median = centroid - altitude = orthocenter