| A | B |
|---|
| Shortest Distance Conjecture | the shortest distance from a point to a line is measured along the perpendicular from the point to the line. |
| Distance from a point to a line | the length of the perpendicular segment from the point to the line. |
| Altitude (of a triangle | a perpendicular segment from the vertex to the opposite side or to a line containing the opposite side. |
| Angle Bisector | divides an angle into two congruent angles. |
| Angle Bisector Conjecture | If a point is on the bisector of a n angle, then it is the same distance from the sides of the angle. |
| Parallel Slope Property | In a coordinate plane, two distinct lines are parallel if and only if their slopes are equal. |
| Perpendicular Slope Property | In a coordinate plane, two nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. |
| Concurrent | three or more lines have a point in common |
| Point of Concurrency | the point of intersection. |
| Angle Bisector Concurrency Conjecture | the three angle bisectors of a triangle are concurrent. |
| Perpendicular Bisector Concurrency Conjecture | the three perpendicular bisectors of a triangle are concurrent. |
| Altitude Concurrency Conjecture | the three altitudes (or the lines containing the altitudes) of a triangle are concurrent. |
| Incenter | the point of concurrency for the three angle bisectors |
| Circumcenter | the point of concurrency for the three perpendicular bisectors. |
| Orthocenter | the point of con currency for the three altitudes |
| Circumcenter Conjecture | the circumcenter of a triangle is equidistant from all three vertices. |
| Incenter Conjecture | the incenter of a triangle is equidistant from all three sides. |
| Circumscribed | a circle is circumscribed about a polygon if and only if it passes through each vertex of the polygon. |
| Inscribed | a circle is inscribed in a polygon if and only if it touches each side of the polygon at exactly one point. |
| Median Concurrency Conjecture | the three medians of a triangle are concurrent. |
| Centroid | the point of concurrency of the three medians. |
| Centroid Conjecture | the centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side. |
| Center of Gravity | the balancing point of a triangle. |
| Center of Gravity Conjecture | the centroid of a triangle is the center of gravity of the triangular region. |
