Download Guided Notes - Exploring Right Triangles

Geometry
Guided Notes
Exploring Right Triangles
Parts of a right triangle:
Name: _________________________
Date: ________________ Period: ___
All right triangles are isosceles or scalene. (No right triangle is obtuse, acute, or equilateral.)
Similar Triangles
Theorem - 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.
Example #1: ̅̅̅̅ is an altitude of ΔABC. Name the three similar triangles.
L: ___ ___ ___
1. _________ ~ _________
M: ___ ___ ___
2. _________ ~ _________
S: ___ ___ ___
3. _________ ~ _________
Geometric Mean
The geometric mean of two numbers a and b is the positive number x such that
Example #2: Find the geometric mean of 3 and 10.
Example #3: Find the geometric mean of 2 and 18.
Solving Right Triangles Using the Geometric Mean
Theorem - In a right triangle, the length of the altitude from the right angle to the hypotenuse is the geometric
mean of the lengths of the two segments of the hypotenuse.
____________________
Example #4: Solve for x.
Geometry
Name: _________________________
Guided Notes
Exploring Right Triangles
Date: ________________ Period: ___
Theorem - In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into
two segments. Each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the
hypotenuse that is adjacent to the leg.
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Example #5:
The segment of the hypotenuse that is adjacent to leg ______ is ______
2
x
24
The segment of the hypotenuse that is adjacent to leg ______ is ______
Example #6:
Example #7:
Example #8:
Example #9:
Example #10:
Example #11: