| A | B |
|---|
| A point is equidistant from two points | if its distance from each point is the same. |
| Perpendicular bisector | A segment, ray, line, or plane that is perpendicular to a segment at its midpoint |
| Distance from a point to a line | length of the perpendicular segment from the point to the line |
| Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. |
| Converse of the Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |
| 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 the Angle Bisector Theorem | If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. |
| Perpendicular bisector of a triangle | a line (or ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side. |
| Concurrent lines (or rays or segments) | when three or more lines (or rays or segments) intersect in the same point |
| Point of concurrency | the point of intersection of concurrent lines |
| Circumcenter of the triangle | the point of concurrency of the perpendicular bisectors of a triangle |
| Angle bisector of a triangle | bisector of an angle of the triangle |
| Incenter of the triangle | the point of concurrency of the angle bisectors |
| Concurrency of Perpendicular Bisectors of a Triangle | The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. |
| Concurrency of Angle Bisectors of a Triangle | The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. |
| Median of a triangle | a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. |
| Centroid of the triangle | the point of concurrency of the three medians of a triangle |
| Altitude of a triangle | the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side. |
| Orthocenter of the triangle | The point where the lines containing the three altitudes are concurrent |
| Concurrency of Medians of a Triangle | The medians of a triangle are concurrent at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. |
| Concurrency of Altitudes of a Triangle | The lines containing the altitudes of a triangle are concurrent. |
| Midsegment of a triangle | a segment that connects the midpoints of two sides of a triangle. |
| Midsegment Theorem | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. |
| If one side of a triangle is longer than another side, then the angle opposite the longer side | is larger than the angle opposite the shorter side. |
| If one angle of a triangle is larger than another angle, then the side opposite the larger | angle is longer than the side opposite the smaller angle. |
| Exterior Angle Inequality | The measure of an exterior angle of a triangle is greater than the measure of either of the two on adjacent interior angles. |
| Triangle Inequality | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| Indirect proof | a proof in which you prove that a statement is true by first assuming that its opposite is true. If this assumption leads to an impossibility, then you have proved that the original statement is true. |
| Hinge Theorem | If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. |
| Converse of the Hinge Theorem | If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. |
