Geometry: Chapter 8 Flashcards
Theorem 8-1
if the altitude is drawn to the hypotenuse of a right triangle, then the two triangle formed are similar to the original triangle and eachother.
geometric mean
the squareroot of the multiplication of two numbers
a/x=x/b
Corollary 1 of Theorem 8-1
When the altitude is drawn to the hypotenuse of a right triangle then the length of the altitude is the geometric mean between the segments of the hypotenuse
Corollary 2 of Theorem 8-1
When the altitude is drawn to the hypotenuse of a right triangle each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to the leg
Theorem 8-2 Pythagorean Theorem
in a right triangle the square of the hypotenuse is equal to the sum of the squares of the legs
Theorem 8-3
If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a right triangle.
Theorem 8-3
If the square of the longest side is equal to the sum of the squares of the other two sides then the angle opposite the longest side is 90 degrees and the triangle is right
Theorem 8-4
if the square of the longest side is less than the sum of the squares of the other two sides then the angle opposite the longest side is less than 90 degrees and the triangle is acute
Theorem 8-5
If the square of the longest side is greater than the sum of the squares of the two other sides then the angle opposite the longest side is greater than 90 degrees and the triangle is obtuse
Theorem 8-4
45-45-90 Theorem
in a 45-45-90 degree triangle the hypotenuse is rad. 2 times as long as a leg
Theorem 8-7
30-60-90 theorem
in a 30-60-90 triangle the hypotenuse is twice as long as the shorter leg and the longer leg is rad. 3 times as long as the shorter leg
tangent
tan(A= opposite/adjacent
