21 terms

Yeah this is for ze test on um like Wednesday that I personally failed...... yeah

perpendicular bisector

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.

circumcenter

the point at where the perpendicular bisectors of a segment intersect

circumscribed

the circumcenter of a triangle is the center of the ______ circle of the triangle

circumcenter theorem

the circumcenter of a triangle is equidistant to the verticies of the triangle.

angle bisector

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.

incenter

Angle bisectors of a triangle intersect at a single point called an ________. The ______ is the center of the inscribed circle of the triangle.

incenter theorem

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.

perpendicular bisector

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.

Pythagorean theorem

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.