Geometry Chapter 8 Part 1

• Pythagorean Triples - Nonzero whole numbers, a, b, and c such that A^2 + b^2 = c^2
• If c^2 < a^2+b^2, then the triangle is acute
• If c^2 > a^2+b^2, then the triangle is obtuse
• Right Triangle Similarity 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 eachother
• Geometric Mean (Altitude) Theorem - In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments; The length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse
• Geometric Mean (Leg) Theorem - In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg altitude
• Geometric Mean: x/r = s/x