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

Thrm. 5-10

If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side

Thrm. 5-11

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

Equidistant

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

Concurrent

When 3 or more lines intersect at one point

Point of Concurrency

Point at which three or more lines intersect

Circumcenter

Point of concurrency of perpendicular bisectors of a triangle

Circumscribed about

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

Incenter

Point of concurrency of the angle bisectors of a triangle

Inscribed in

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?

3 medians