Geometry 8.1, Similarity in Right Triangles

An explanation of how the altitude drawn from the vertex of a right triangle to the hypotenuse forms two right triangles. A theorem (8.1.1) about an altitude drawn to the hypotenuse of a right triangle will form two similar triangles, and a we do a proof of that theorem. We discuss the geometric mean of two positive numbers is the positive square root of their product. We find the geometric mean of a pair of numbers and write them in simplest radical form. We use our theorem to write proportions comparing the side lengths of right triangles formed by the altitude to the hypotenuse. Geometric Means Corollaries 8.1.2 and 8.1.3 are used to help us find an altitude x, leg b, and leg a of a right triangle. We estimate the height of a statue using the corollaries.

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[yasminothman]

Thank you so much for this amazing explanation! 👌