21 terms

# Chapter 5 Geometry

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midsegments of a triangle
a segment that connects the midpoints of two sides of the triangle
midsegment theorm
the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side
perpendicular bisecter
a segment, ray, line that is perpendicular to a segment at its midpoint
perpendicular bisector theorm
in a plane, if a point is on the perpendicular bisector of a segment, then it is equidstant from the endpoints of the segment
converse of the perpendicular bisector theorm
in a plane, if a point is equidisant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
concurrent lines
three or more lines, rays, or segments that intersect at the same point
point of currency
the point of intersection
concurrency of perpendicular bisector of a triangle
the perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle
circumcenter
the point of concurrency of the three perpendicular bisectors of a trianlge (equidstant from the three vertices)
angle bisector
rays that divides an angle into two adjacent, congruent angles
angle bisector theorm
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
converse of the angle bisector theorm
if a point is in the interior of an angle and is equidstant from the sides of the angle, then it lies on the angle bisector of the angle
concurrency of angle bisectors of a triangle
the angle bisector of a triangle intersect at a point that is equidistant from the sides of a triangle
incenter
the poing of concurrency of the three angle bisectors of a triangle (always lies inside the triangle)
median of a triangle
a segment from a vertex to the midpoint of the opposite side
centroid
the point of concurrency of the medians (inside the two angles)
concurrency of medians of a triangle
the medians of a triangle intersect at a point that is 2/3 of the distance from the vertex to the midpoint of the opposite side
altitude
the perpendicular segment from the vertex to the opposite side or to the line that contains the opposite side
concurrency of altitudes of a triangle
the lines containing the altitudes of a triangle are concurrent
orthocenter
the point at which the lines containing the three alltitudes intersect
triangle inequality theorm
the sum of the lengthsw of any tow sides of a triangle is greater than the length of the third side