Question | Answer |
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 |
Converse of Pythagorean Theorem | 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 |
Geometric Mean (Altitude) Theorem | 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 |
45-45-90 Triangle Theorem | In a 45-45-90 triangle, the hypotenuse is the square root of 2 times as long as each leg |
30-60-90 Triangle Theorem | in a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg |
| 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 |
| 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 |
| If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other |
Geometric Mean (Leg) Theorem | in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments; the length of each leg of the right triangle is the geometric mean of the lengths of hypotenuse and the segment of the hypotenuse that is |
| adjacent to the leg |