Chapter 5 Flashcards
(25 cards)
a line segment that oins the midpoints of 2 sides of a triangle
midsegment
a midsegment of a triangle is parallel to the third side of the triangle and its length is equal to half the length of the third side
midsegment theorem
placing geometric figures in a coordinate plane to prove something
coordinate proof
a segment, ray, or line that is perpendicular to a given segment at its midpoint
perpendicular bisector
if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
perpendicular bisector theorem
if a point is equidistant from the endpoints of a segment, then it in on the perpendicular bisector of the segment
converse of the perpendicular bisector theorem
when 3 lines, rays, or segments meet at the same point
concurrent
the point of intersection of lines, rays, or segments
point of concurrency
the per. bisectors of atriangle intersect at a point that is equidistant from the vertices of a triangle
concurrency of perpendicular bisectors of a triangle
the point hwere the 3 perp. bisectors of a triangle meet
circumcenter
since the circumcenter is equidistant from all 3 vertices, it is the center of a circle that contains all 3 vertices of a triangle called
circumcircle
ray that divides an angle into two congruent adjacent angles
angle bisector
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
angle bisector theorem
the length of a perp. segment drawn from the point to the line
the distance from a point to a line
if a point is in the interior of an angle and is equidistant from the sides of the triangle, then it lies on the bisector of the angle
converse of the angle bisector theorem
the angle bisectors of a triangle meet at a point that is equidistant from the sides of the triangle
concurrency of the angle bisector of a triangle
point of concurrency of angle bisectors of a triangle
incenter
circle that has a radius equal to the distance from the incenter to the sides of the triangle
incircle
the segment joining a vertex and the midpoint of the opposite side
median
the point of concurrency of the medians of a triangle
centroid
balancing point of a triangle
centroid
the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side
concurrency of the medians of a triangle
perp. segment from a vertex to the opposite side
altitude
height of the triangle
orthocenter
