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segment connecting the midpoints of two sides of the triangle

mid segment of a triangle

1

theorem- if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long

5-1 triangle mid segment theorem

2

a point from two objects that is the same distance from both objects

equidistant

3

theorem- if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint if the segment

5-2 perpendicular bisector theorem

4

theorem- if a point is equidistant from the endpoints of the seventh then is on the perpendicular bisector of a segment

5-3 converse perpendicular bisector theorem

5

theorem- if a point is on the bisector of an angle, then the points is equidistant from the sides of the angle

5-4 angle bisector theorem

6

theorem- if a point in the interior of an angle is equidistant from the side of the angle, then the point is on the angle bisector

5-5 converse angle bisector theorem

7

when three or more lines intersect at one point

concurrent

8

the pint at which they interest

point of concurrency

9

theorem- the perpendicular bisectors of a triangle are congruent at a point equidistant from the vertices

5-6 concurrency of perpendicular bisectors theorem

10

the point of concurrency of the perpendicular bisector of a triangle

circumcenter

11

the circumcenter of a triangle can be

inside outside or on a triangle

12

the point of concurrency of the angle bisectors of a triangle

incenter of the triangle

13

theorem- the bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle

5-7 concurrency of angle bisector theorem