Term
Theorem
If the altitude is drawn to the hypotenuse of a right trianlge, then... |
|
Definition
Theorem
...then the two triangles formed are similar to the origininal triangle and to each other |
|
|
Term
Corollary
When the altitude is drawn to the hypotenuseof a right trianlge, the length of the altitude... |
|
Definition
Corollary
...the length of the altitude is the geometric mean between the segments of the hypotenuse. |
|
|
Term
Corollary
When the altitude is drawn to the hypotenuse of a right triangle, each leg... |
|
Definition
Corollary
...each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. |
|
|
Term
Pythagorean Theorem
In a right trianlge, the square of the hypotenuse is equal to... |
|
Definition
Pythagorean Theorem
the sum of the squares of the legs.
a2+b2=c2 |
|
|
Term
Converse of the Pythagorean Theorem
If the square of one side of a triangle is equal to the sum of the square of the other two sides, then... |
|
Definition
Converse of the Pythagorean Theorem
...then the triangle is a right triangle
If a2+b2=c2, then it is a right trianlge |
|
|
Term
|
Definition
A set of nonzero whole numbers that "work" in the pythagorean theorem
3,4,5
5,12,13
8,15,17
7,24,25 |
|
|
Term
Theorem
If the square of the length of the longes side of a triangle is greater than the sum of the square of the length of teh other two sides, then... |
|
Definition
Theorem
...then the trianlge is obtuse.
If c2>a2+b2, then the triangle is obtuse |
|
|
Term
Theorem
If teh squareof 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... |
|
Definition
Theorem
...then the triangle is acute.
If c2<a2+b2, then the triangle is acute. |
|
|
