Honors Geometry Special Segments

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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


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