Similarity in Right Triangles Flashcards
What is the arithmetic mean?
“If all the qualities had the same value, what would that value be in order to achieve the same total (sum)?”
Ex. What is the arithmetic mean of 3, 4, 5, 6 ?
3+4+5+6/4 = 4.5
4.5 + 4.5 + 4.5 + 4.5 = 18 = 3 + 4 + 5 + 6
What is the geometric mean?
“if all the quantities had the same value, what would that value have to be in order to achieve the same product?”
Ex. What is the geometric mean of 5, 10?
5 x 10 = x x x ⇒ 50 = x^2
√50 = x
√50 = 25√2
How would you solve the geometic menan of 3, 4, 6, 8?
- Multply set of numbers under the radical, if its not a perfect square then keep it broken up
^4√(3 x 4 x 6 x 8)
- Put multiplied numbers under the correspndong radical for number of numbers in a set. Break up radical to easy landmark roots
^2√^2√( 3 x 4 (3 x 2) x (4 x 2))
√(4 x 2 x 3)
√24
2√6
What is theorem 8 - 1?
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.
What is corollary 1 for Theorem 8 - 1?
When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.
What is corollary 2 for 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 that leg.
