Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
(Sect. 5­1) ­ Bisectors of Triangles
Perpendicular Bisector ­ a segment that not only
bisects another segment, but is also perpendicular to it.
Perpendicular Bisector Theorem (5.1) ­
If a point is on the perpendicular bisector of
a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Theorem ­
(5.2) If a point is equidistant from the endpoints
of a segment, then it is on the perpendicular
bisector of the segment.
Mr. VanKeuren / G.H.S. / Mar 2015
1
Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
Concurrent Lines ­ three or more lines that
intersect at a common point.
Point of Concurrency ­ the point where the concurrent lines intersect.
Circumcenter ­ the point of concurrency for the
three perpendicular bisectors of the sides of
a triangle.
Point P is the
circumcenter of
triangle ABC
Mr. VanKeuren / G.H.S. / Mar 2015
2
Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
Circumcenter Theorem ­
The perpendicular bisectors of a triangle
intersect at a point called the circumcenter
that is equidistant from the vertices of the
triangle.
Mr. VanKeuren / G.H.S. / Mar 2015
3
Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
*The circumcenter can be on the interior,
exterior, or side of the triangle.
Remember, these lines are the perpendicular
bisectors of the sides of the triangle.
Mr. VanKeuren / G.H.S. / Mar 2015
4
Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
Angle Bisector Theorem ­
If a point is on the bisector of an angle, then
it is equidistant form the sides of the angle.
DF = FE
Converse of the Angle Bisector Theorem ­
If a point in the interior of an angle is
equidistant from the sides of the angle. then
it is on the bisector of the angle.
Mr. VanKeuren / G.H.S. / Mar 2015
5
Sect. 5.1
G.CO.10 / G.MG.3 / Math Pract. 1,3
Incenter ­ the point of concurrency for the angle bisectors of a triangle
Incenter Theorem ­
The angle bisectors of a triangle intersect
at a point called the incenter that is
equidistant from the sides of the triangle.
Mr. VanKeuren / G.H.S. / Mar 2015
6