Similar Triangles in Circles and Right Triangles
More Lessons for High School Regents Exam
Math Worksheets
High School Math based on the topics required for the Regents Exam conducted by NYSED.
The following diagram shows geometric mean of similar right triangles: Altitude Rule, Leg Rule. Scroll down the page for more examples and solutions for the Geometric Mean Theorem.
Two triangles in a circle are similar if two pairs of angles have the same intercepted arc. Sharing an intercepted arc means the inscribed angles are congruent. Since these angles are congruent, the triangles are similar by the AA shortcut.
If an altitude is drawn from the right angle in a right triangle, three similar triangles are formed, also because of the AA shortcut.
This video shows what the geometric mean is and how it is applied to similar right triangles. Right triangle similarity examples are demonstrated with and without formulas.
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