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Theorem 8-1-1

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.

Corollaries 8-1-2 Geometric means

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Corollary 8-1-3 Geometric means

the length of a leg of a right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

Theorem 8-5-1 The Law of Sines

For any ΔABC with side lengths a, b, and c, sin A / a = sin B / b = sin C / c.

Theorem 8-5-2 The Law of Cosines

For any ΔABC with sides a, b, and c, a² = b² + c² - 2bc cosA, b² = a² + c² - 2ac cosB, and c² = a² + b² - 2ab cosC