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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. ____________________ ____________________ 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: