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Part 12

 Corollary 2 The volume of a cone with a base radius of length r and an altitude of length h is 1/3P r^2h. Theorem 14.10 The volume of a sphere with radius of length r is 4/3Pr^3. Theorem 14.11 The area of a sphere is 4Pr^2. Theorem 14.12 The distance between points P(x1, y1, z1) and Q(x2, y2, z2) is given by the formula d = Ö(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2. Theorem 15.1 A reflection is an isometry. Theorem 15.2 A translation is an isometry. Theorem 15.3 The resultant image determined by two successive reflections about parallel lines is a translation. Theorem 15.4 A rotation is an isometry. Theorem 15.5 The measure of the angle of rotation formed by two successive reflections (or by the product of two reflections) is twice the measure of the non-obtuse angle between the two lines of symmetry. Theorem 15.6 The transformation defined by adding a constant to the coordinates of each point is a translation. Theorem 15.7 The transformation defined by multiplying each coordinate of each point by a constant is a dilation.

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Note: The concepts in this collection may not be entirely accurate.
They are for reference only.