5.2 Special Segments of a Triangle Flashcards
Angle Bisector of a Triangle
a segment that bisects one of the angles in the triangle
every triangle has 3 angles bisectors
it has to go through a vertex of the triangle
Perpendicular Bisector of an Triangle
a segment that is part of a perpendicular bisector of one of the sides
every triangle has 3 perpendicular bisectors
does not have to have a vertex of the triangle to be one of the end points
median
a segment whose endpoints are a VERTEX and the MIDPOINT of the opposite side of the triangle
every triangle has 3 medians
has to go through a vertex
can also be a perpendicular bisector
altitude
a segment from the vertex that is perpendicular to the opposite side or the line containing the opposite side
every triangle have 3 altitudes
doesn’t always lie within the triangle
endpoint has to be a vertex
in an isosceles triangle…
the perpendicular bisector, angles bisector, median, and altitude FROM THE VERTEX ANGLE (non-base angle) TO THE BASE are the same exact segment
in an equilateral triangle…
the perpendicular bisector, angle bisector, median, and altitude FROM ANY ONE VERTEX are the same exact segment
concurrent
two or more lines are concurrent if they intersect at a single point
circumcenter goes with WHAT?
point of currency for 3 perpendicular bisectors of a triangle
PBCC(peanut butter and creamcheese)
PERPENDICULAR BISECTOR
incenter goes with WHAT?
point of concurrency for 3 angle bisectors of a triangle
ABIC(apple banana ice cream)
ANGLE BISECTOR
centroid goes with WHAT?
point of concurrency for 3 medians in a triangle
MC(macaroni and cheese)
MEDIANS
orthocenter goes with WHAT?
point of concurrency for 3 altitudes in a triangle
AO(apples and oranges)
ALTITUDES
congruence property for circumcenter
the circumcenter is equidistant from the three vertices of the triangle
congruence property for incenter
the incenter is equidistant from the three sides of the triangle (measured along segments that are perpendicular to the the sides of the triangle)
congruence property with centroid
the distance from any vertex to the centroid is 2/3 of the distance from the vertex to the midpoint of the opposite side
