A line that intersects a given segment at right angles and divides it into two equal parts
perpendicular bisector theorem
If a point is on the perpendicular bisector of a segment, then the point equidistant from the endpoints of the segment.
converse of perpendicular bisector theorem
If a point is equidistant to the endpoints of a segment, then it is on the perpendicular bisector.
the point at where the perpendicular bisectors of a segment intersect
the circumcenter of a triangle is the center of the ______ circle of the triangle
the circumcenter of a triangle is equidistant to the verticies of the triangle.
a ray that divides an angle into two congruent angles
angle bisector theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
converse of angle bisector theorem
If a point is in the interior of an angle and it is equidistant from the sides of the angle, then it lies on the bisector of the angle.
Angle bisectors of a triangle intersect at a single point called an ________. The ______ is the center of the inscribed circle of the triangle.
the incenter of a triangle is equidistant to the sides of the triangle.
altitude of a triangle
a segment from a vertex that is perpendicular to the opposite side.
median of a triangle
a segment from a vertex to the midpoint of an opposite side.
a line perpendicular to a segment at the segments midpoint.
centroid of a triangle
the point of concurrency of the three medians of a triangle
circumcenter of a triangle
the point of concurrency of the three perpendicular bisectors of a triangle
orthocenter of a triangle
the point of concurrency of the three altitudes of a triangle.
midsegment of a triangle
a segment that joins the midpoints of two sides of a triangle.
triangle midsegment theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length
triangle inequality theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.