Geometric Mean / Similarity in Right Triangles
L.T. I can use relationships in ______________ ____________ triangles.
Simplifying Radicals
Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81…
Find the largest Perfect Square that goes into the number evenly
example: 72 The largest Perfect Square that goes into 72 is _____.
What if you picked 9 instead of 36?
If you pick a smaller Perfect Square you must reduce more than once.
example: 72 9 is a Perfect Square that goes into 72 evenly, though not the largest
Geometric Mean
If a, b, and x are positive numbers and __________ , then x is called the geometric mean between a and b.
Example: Find the geometric mean of 3 and 12.
Right Triangle Similarity Theorem
If the _____________ is drawn to the __________________of a right triangle, then the two triangles formed are ____________to the
original triangle and each other.
Similarity in Right Triangles - Corollary 1
The length of the altitude of the right triangle is the geometric mean between the segments of the hypotenuse .
Example: Find the length of the altitude.
Similarity in Right Triangles – Corollary 2
Each leg of the right triangle is the geometric mean between the hypotenuse and the segment of the hypotenuse
adjacent to the leg.
Example: Find the length of the leg.
2
y
5
More Practice
Find the values of x and y.