# Section 7 by HC121104002213

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```									 Geometry                                                                                 Notes #:
Section 7.4: Similarity in Right Triangles                 Objective:

Theorem 7-3: The altitude to the hypotenuse of a right
triangle divides the triangle into 2 triangles that are
similar to the original triangle and to each other.

Corollary 2: The altitude to the hypotenuse of a
Corollary 1: The length of the altitude           right triangle separates the hypotenuse so that the
to the hypotenuse of a right triangle is          length of each leg of the triangle is the geometric
the geometric mean of the lengths of the          mean of the length of the hypotenuse and the length
segments of the hypotenuse.                       of the segment of the hypotenuse adjacent to the leg.
(BOOMERANG METHOD)                                (SOCK METHOD)

Example 1) Find the geometric mean of 4 and 18.
Geometric Mean:
Where x is the
geometric mean

Example 2) What similarity statement can you
write relating the 3 triangles in the diagram?          Example 3) What are the values of x and y?
Geometry                                                                           Notes #:
Section 7.4: Similarity in Right Triangles             Objective:

Example 4) Maggie has a kite with the dimensions shown below.
What is the width of the kite?

To simplify a radical, come up with
two factors of that number. One of
SIMPLIFYING RADICALS                           them must be the largest perfect
square that goes into that number.
Break it into two square roots and
then simplify!

Example 5) Simplify

Example 6) Simplify

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