Honors Geometry Special Segments
The ________ divides each median into two sections at a 2 to 1 ratio
Centroid
a median _ has a mdpt as an endpoint
always
in a _ triangle, the altitudes are the legs
right
Perpendicular segment from a vertex of a triangle to its opposite side of the line that contains its opposite side
Altitude
A ray that bisects an Ingle and is equidistant from the sides of the triangle
Angle bisector
The three medians of a triangle intersect at the
Centroid
The three perpendicular bisectors of a triangle intersect at the
Circumcenter
The three angle bisectors of a triangle intersect at the
Incenter
a segment that connects the midpoints of two sides of a triangle
Midsegment
The three altitudes of a triangle intersect at the
Orthocenter
A midsegment of a triangle will ________ be parallel to one side of the triangle
always
An altitude of a triangle is _________ perpendicular to a side of a triangle
always
The in center of a right triangle is _______ on the triangle
always
The points of concurrency of the three perpendicular bisectors is ______ called the circumcenter
always
centroids are _____ on the interior of a triangle
always
each leg of a right triangle _ an altitude of the triangle
always
each leg of a right triangle is _ an altitude of the triangle
always
in an obtuse triangle, the orthocenter is _____ outside the triangle
always
in an obtuse triangle, two altitudes are _ outside the triangle
always
the Altitude of an acute triangle ______ Intersect in the interior of the triangle
always
the angle bisectors of a triangle _ intersect at a single point
always
the centroid is _ inside the triangle
always
the median from the vertex angle of an isosceles triangle is _ the same segment as the altitude from the same vertex
always
the medians of a triangle ______ fall inside the triangle
always
two of the altitude of a right triangle are _ the legs of the triangle
always
the _ divides the median into two sections that have a 2:1 ratio
centroid
the _ is 2/3 the distance of the median from the vertex
centroid
the medians meet at the
centroid
The ________ is equidistant from the three vertices of the triangle
circumcenter
the _ is equidistant from the vertices of the triangle
circumcenter
the perpendicular bisectors meet at the
circumcenter
The _____ is equidistant from the three sides of the triangle
incenter
the _ is equidistant from the sides of the triangle
incenter
the angle bisectors meet at the
incenter
A segment whose points are a vertex of the triangle in the middle point of the opposite side
median
The angle bisector of a triangle ______ intersects at a point outside the triangle
never
The perimeter of a triangle formed by the midsegment of a triangle is ______ twice the original triangle's perimeter
never
The perpendicular bisector of a triangle ca ________ be a side of the triangle
never
a circumcenter is _______ equidistant from the sides of a triangle
never
the circumcenter and the orthocenter can _ be the same point
never
the incenter of an obscure triangle is _ outside the triangle
never
the three angle bisectors of a triangle _ intersect at a point that is outside the triangle
never
the orthocenter is located _ of an obtuse triangle
outside
A segment, Ray, line, or plane that is perpendicular to a segment at its midpoint
perpendicular bisector
to find the point that is equidistant from the vertices of a triangle, we need to find the three _ of the triangle
perpendicular bisectors
A median is _ perpendicular to the opposite side
sometimes
A perpendicular bisector of a triangle ________ passes through the opposite vertex
sometimes
Median and angle bisectors _____ the same segment in a triangle
sometimes
The altitude of a triangle can ______ be a side of a triangle
sometimes
The altitude of a triangle is ______ through the midpoint of a side of a triangle
sometimes
The angle bisector of a triangle ______ bisects the other side
sometimes
The circumcenter or of a scalene triangle is ______ inside the triangle
sometimes
The median and the altitude from a vertex of a triangle are _______ The same segment
sometimes
The point of concurrency of three perpendicular bisectors is _______ inside the triangle
sometimes
a perpendicular bisector _ has a vertex as an endpoint
sometimes
an altitude is _ an angle bisector
sometimes
an altitude_ lies outside a trianglr
sometimes
if line AM is an altitude of triangle ANC, then line AM is _ a median of the triangle
sometimes
orthocenters are _______ inside the triangle
sometimes
the angle bisectors of a triangle _ bisect the sides of the triangle
sometimes
the three altitudes if a triangle _ intersect at a point that is inside the triangle
sometimes
