Download Advanced Geometry LT 5.3 - Identify similar right triangles formed by

Advanced Geometry
LT 5.3 - Identify similar right triangles formed by the
altitude drawn to the hypotenuse and use those
properties to solve problems
Finding Geometric Means of Pairs of Numbers
The geometric mean of two positive numbers is the positive square root of their product.
Example 1:
Find the geometric mean of each pair of numbers.
a) 4 and 25
b) 9 and 20
c) 5 and 12
Exploring the Geometric Mean Theorems
Use tracing paper to compare the angles of triangles 1, 2, and 3. (Trace one of the triangles to start)
What do you notice about the angles?
What does this tell you about the triangles? Why?
Similarity in Right Triangles
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the
original triangle.
Geometric Mean Theorems
 The length of the altitude to the hypotenuse of a right triangle is
the geometric mean of the lengths of the segments of the
hypotenuse

The length of a leg of a right triangle is the geometric mean of the
lengths of the hypotenuse and the segment of the hypotenuse
adjacent to that leg
Example 2:
Write similarity statements comparing the three triangles in each diagram.
a)
b)
Example 3:
Find the value of each variable.
a)
b)
c)
Practice
Find the geometric mean x of each pair of numbers. Give answers in simplest radical form.
1. 3 and 12
2. 8 and 13
3. 2 and 8
Write a similarity statement comparing the three triangles in each diagram.
4.
5.
Find the value of all variables. Give answers in simplest radical form.
6.
7.
8.
9. Round to the nearest tenth.
11.
10.