| A | B |
|---|
| Pythagorean Theorem | In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. |
| right triangle | Any triangle that has one right angle. |
| hypotenuse | The longest side of a right triangle; it the side opposite the right angle. |
| leg | A side of a right triangle that is not the hypotenuse. |
| geometric mean | a/x=x/b |
| Pythagorean triple | A set of three positive integers that satisfy the Pythagorean Theorem. |
| Pythagorean Converse | If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. |
| obtuse triangle | If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle. |
| acute triangle | If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle. |
| altitude | A segment extending from the vertex perpendicular to the opposite side or the line containing the opposite side of a triangle. |
| similar triangles | Two triangles whose corresponding angles are congruent and corresponding sides are proprotional. |
| Geometric Mean (Altitude) Theorem | In a right triangle with an altitude drawn to the hypotenuse, the length of the altitude is the geometric mean of the length of the two pieces of the hypotenuse. |
| Geometric Mean (Leg) Theorem | In a right triangle with an altitude drawn to the hypotenuse, the length of each leg is the geometric mean of the entire hypotenuse and the piece of the hypotenuse adjacent to that leg. |
| isosceles triangle | A triangle with two congruent sides. |
| equilateral triangle | A triangle with three congruent sides. |
| scalene triangle | A triangle with no congruent sides. |
| 45-45-90 | A special right triangle whose hypotenuse is square root of two times as long as each leg. |
| 30-60-90 | A special right triangle whose hypotenuse is twice as long as the shorter leg, and whose longer leg is square root of three times as long as the shorter leg. |
| tangent | opposite/adjacent |
| trigonometric ratio | A ratio of the lengths of two sies in a right triangle. They are used to find the measure of a side or an acute angle in a right triangle. |
| sine | opposite/hypotenuse |
| cosine | adjacent/hypotenuse |
| inverse trigonometric ratio | When two sides of a right triangle are known, this is used to find the measure of an acute angle in the right triangle. |
