[Table 2-1] Other centers of tetrahedron Position in Position in Centers 2D Geometry 3D Geometry Circumcenter A point where three A point where perpendicular

bisectors perpendicular bisecting intersect planes intersect Centroid A point where three A point where median medians intersect planes (Planes with a edge and its opposite edge's middle point) intersect Excenter A point where exterior A point where exterior angle

bisectors intersect dihedral-bisecting planes intersect Centers Property Circumcenter Becomes the center of the circumcircle and the circumsphere, respectively Centroid Divides the line which connects a point and the opposite planes' centroid as 2:1, 3:1 respectively Excenter Becomes the center of the excircle and the exosphere, respectively

An angle

bisector at vertex A of the parallelogram ABCD meets the straight lines BC and CD at the points K and L respectively.

For instance, the points equidistant from two points A and B are on the perpendicular

bisector of the segment AB.

It is worth noting that prior to or in the course of making this proof, students can fold perpendicular

bisectors to the base in non isosceles triangles to "establish" that only in isosceles triangles does the perpendicular

bisector pass through the opposite vertex.

we obtain that the equations of their angle

bisectors are:

Each cell may be perceived as the intersection of open half-planes bounded by the perpendicular

bisectors of lines joining one inclusion center with each of its neighbors.

The intersection point of two perpendicular

bisectors of the chords is regarded as the estimated position of sensor node.

Caption: Figure 9: Construction of the circle, using the perpendicular

bisectors [P.sub.o][P.sub.v] and [P.sub.o][P.sub.f].

During the initial sessions in the first year, the participants examined some animations created by the research team with examples of two problem-based lessons about perpendicular

bisectors. The animations illustrated students' work and teaching actions for using students' prior knowledge in those lessons (Gonzalez & DeJarnette, 2016).

The Dirichlet domain of [GAMMA] is based on the

bisectors of some chosen center and its images by [GAMMA].

And the perpendicular

bisectors of each side intersect at a single point called the circumcenter?