| A | B |
|---|
| Median of a triangle | A segment that connects a vertex of a triangle to the midpoint of the opposite side. |
| Altitude | A segment that has one endpoint at a vertex of a triangle and the other on the line that contains the side opposite that vertex so that the segment is perpendicular to this line (height) |
| Angle bisector of a triangle | A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint at another point on the triangle |
| Perpendicular bisector | A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side |
| A point on the perpendicular bisector of a segment is... | equidistant from the endpoints of the segment |
| A point equidistant from the endpoints of a segment... | lies on the perpendicular bisector of the segment |
| A point on the angle bisector of an angle... | is equidistant from the sides of the triangle |
| A point in the interior of an angle and equidistant from the sides of an angle... | lies on the bisector of the angle. |
| HL | Hypotenuse/Leg - a way to prove right triangles are congruent |
| Indirect proof step one | assume the conclusion is false. |
| Definition of inequality | For any real numbers a and b, a>b if there is a positive number c such that a=b+c |
| Exterior angle inequality theorem | If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its remote interior angles. |
| BSBA | If one side of a triangle is longer than another side, then the angle opposite the longer side is greater than the angle opposite the shorter side |
| BABS | If one angle of a triangle is greater than another angle, then side opposite the greater angle is longer than the side opposite the lesser angle. |
| The perpendicular segment from a point to a line is... | the shortest segment from the point to the line |
| Triangle inequality theorem | The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side |
| SAS Inequality theorem | If two sides of one triangle are congruent to two sides of another triangle, and the included angle is one triangle is greater than the included angle of the other, then the third side of the first triangle is longer than the third side of the second triangle. |
| SSS Inequality theorem | If two sides of one triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding included angle in the second triangle. |
| What are the two theorems that compare sides and angles in ONE triangle | BSBA, BABS |
| What are the two theorems that compare sides and angles in TWO triangle | SAS Inequality, SSS Inequality |
