Triangle Midsegment Thrm.
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long
Perpendicular Bisector Thrm.
If a point is on the perpendicular bisector of a segment, then it is equidistant from the end points of the segment
Converse of Perpendicular Bisector Thrm.
If a point is equidistant from the end points of a segment, then it is on the perpendicular bisector of the segment
Angle Bisector Thrm.
If a point is on the bisector of an angle, then the point is equidistant form the sides of the angle
Converse of Angle Bisector Thrm.
If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector
Concurrency of Perpendicular Bisectors Thrm.
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices
Concurrency of Angle Bisectors Thrm.
The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle
Concurrency of Medians Thrm.
The medians of a triangle are concurrent at a point that is two-thirds the distance from each vertex to the midpoint of the opposite side
Corollary to the Triangle Exterior Angle Thrm.
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles
Concurrency of Altitudes Thrm.
The lines that contain the altitudes of a triangle are concurrent
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side
If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle
Triangle Inequality Thrm.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
*sum of the smallest > than biggest
The Hinge Thrm. (SAS Inequality Thrm.)
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle
Converse of Hinge Thrm.
If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side
Comparison Property of Inequality
If a = b+c and c>0, then a>b
Midsegment of a Triangle
Segment connecting midpoints of two sides of the triangle
A point is equidistant from two objects if it is same distance from objects
Distance from a Point to a Line
Length of the perpendicular segment from the point to the line
When 3 or more lines intersect at one point
Point of Concurrency
Point at which three or more lines intersect
Point of concurrency of perpendicular bisectors of a triangle
Since circumcenter is equidistant from vertices, you can use the circumcenter as the center of the circle that contains each vertex of the triangle
Circle that intersects all vertices of a triangle
Point of concurrency of the angle bisectors of a triangle
Inscribed circle is a circle that is tangent to all sides of the triangle polygon
Median of a Triangle
A segment whose endpoints are a vertex and the midpoint of the opposite side
Centroid of a Triangle
In a triangle, the point of concurrency of the medians
Altitude of a Triangle
Line segment from vertex to opposite side forming right angles
Orthocenter of a Triangle
Point of concurrency (intersection) of three altitudes of a triangle
Circumcenter is constructed by what?
3 perpendicular bisectors
Incenter is constructed by what?
3 angle bisectors
Centroid is constructed by what?