Geometry, Centers of Triangles 

Perpendicular bisector-  A segment, line, ray or plane that is perpendicular (90 degrees) to a segment at its midpointIf a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. 

Circumcenter-  The point of concurrency of the 3 perpendicular bisectors of a triangleThe circumcenter is equidistant from the vertices of a triangle.  The circumcenter will lie inside an acute triangle, at the midpoint of the hypotenuse of a right triangle, or outside an obtuse triangle.The circumcenter can be used to construct a circumscribed circle around the triangle, intersecting all 3 of the triangle’s vertices. 

Angle bisector-  A ray that divides an angle into two adjacent congruent anglesIf a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Incenter-  The point of concurrency of the 3 angle bisectors of a triangleThe incenter of a triangle is equidistant from the sides of the triangle.The incenter can be used to construct the inscribed circle (inside the triangle, touching all 3 sides.) 

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

Centriod-  The point of concurrency of the 3 medians of a triangleThe centroid is two thirds of the distance from each vertex to the midpoint of the opposite side.The centroid is the center of balance of a triangle. 

Altitude of a triangle-  perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.  An altitude can lie inside (if an acute triangle), on (if a right triangle), or outside the triangle (if an obtuse triangle). 

Looking for a math, reading, or writing

tutor in Santa Cruz, Capitola, or Scotts Valley?  

Please check my "current openings " page to see if I am accepting new students.